Half of Israeli Jews have Turkic origin from Central Asia and the Caspian region.

Ashkenazi Jews (50% of Israel Jewish population) are a diaspora who developed in the Middle Ages migrating from the Caspian region westwards to Central and Eastern Europe. All anthropological and linguistic elements indicate that these communities did not come from the Eastern mediterranean region, but from a Caspian Jewish kingdom formed from Turkic ethnic groups migrating west from Central Asia. This kingdom, called Khazaria. adopted judaism as its state religion and it thrived from the 7th to the 10th century. When the kingdom was conquered by the expanding Rus empire, Khazars escaped west and obtained refuge in germanic and slavic countries od Eastern and Central Europe. After cultural and linguistic syncretism these migrating Khazars became what were later called the Ashkenazi Jews.  After the Second World War they started moving to North America and to the recently formed  state of Israel.
It is important to remember that today Azhkenzi jews represent almost half of all Jews of Israel, and of course did not return to any "promised land" of the distant past. 
This helps to understand why the (majority)  traditional inhabitants of Palestine (Israel) are the Palestinians and not the Ashkenazi Jews.
In the Palestine (today Israel) land Ashkenazi are recent newcomers. 
In the following text a brief explanation of the Khazar kingdom is included

Khazaria, a prosperous Jewish kingdom in the Middle Ages

 by Kevin Alan Brook

The history of Khazaria presents us with a fascinating example of how Jewish life flourished in the Middle Ages. In a time when Jews were persecuted thruout Christian Europe, the kingdom of Khazaria was a beacon of hope. Jews were able to flourish in Khazaria because of the tolerance of the Khazar rulers, who invited Byzantine and Persian Jewish refugees to settle in their country. Due to the influence of these refugees, the Khazars found the Jewish religion to be appealing and adopted Judaism in large numbers.

Most of the available information about the Khazars comes from Arabic, Hebrew, Armenian, Byzantine, and Slavic sources, most of which are reliable. There is also a large quantity of archaeological evidence concerning the Khazars that illuminates multiple aspects of the Khazarian economy (arts and crafts, trade, agriculture, fishing, etc.) as well as burial practices.

Origins. The Khazars were a Turkic people who originated in Central Asia. The early Turkic tribes were quite diverse, although it is believed that reddish hair was predominant among them prior to the Mongol conquests. In the beginning, the Khazars believed in Tengri shamanism, spoke a Turkic language, and were nomadic. 
Later, the Khazars adopted Judaism, Islam, and Christianity, learned Hebrew and Slavic, and became settled in cities and towns thruout the north Caucasus and Ukraine. The Khazars had a great history of ethnic independence extending approximately 800 years from the 5th to the 13th century.

The earliest history of the Khazars in southern Russia, prior to the middle of the 6th century, is hidden in obscurity. From about 550 to 630, the Khazars were part of the Western Turkish Empire, ruled by the Celestial Blue Turku (Kök Turks. When the Western Turkish Empire was broken up as a result of civil wars in the middle of the 7th century, the Khazars successfully asserted their independence. Yet, the Kök kaganate under which they had lived provided the Khazars with their system of government. For example, the Khazars followed the same guidelines as the Kök Turks regarding the succession of kings.

Political power. At its maximum extent, the independent country of Khazaria included the geographic regions of southern Russia, northern Caucasus, eastern Ukraine, Crimea, western Kazakhstan, and northwestern Uzbekistan. Other Turkic groups such as the Sabirs and Bulgars came under Khazar jurisdiction during the 7th century. The Khazars forced some of the Bulgars (led by Asparukh) to move to modern-day Bulgaria, while other Bulgars fled to the upper Volga River region where the independent state of Volga Bulgharia was founded. The Khazars had their greatest power over other tribes in the 9th century, controlling eastern Slavs, Magyars, Pechenegs, Burtas, North Caucasian Huns, and other tribes and demanding tribute from them. Because of their jurisdiction over the area, the Caspian Sea was named the "Khazar Sea", and even today the Azeri, Turkish, Persian, and Arabic languages designate the Caspian by this term (in Turkish, "Hazar Denizi"; in Arabic, "Bahr-ul-Khazar"; in Persian, "Daryaye Khazar").

In addition to their role in indirectly bringing about the creation of the modern Balkan nation of Bulgaria, the Khazars played an even more significant role in European affairs. By acting as a buffer state between the Islamic world and the Christian world, Khazaria prevented Islam from significantly spreading north of the Caucasus Mountains. This was accomplished thru a series of wars known as the Arab-Khazar Wars, which took place in the late 7th and early 8th centuries. The wars established the Caucasus and the city of Derbent as the boundary between the Khazars and the Arabs.

Cities. The first Khazar capital was Balanjar, which is identified with the archaeological site Verkhneye Chir-Yurt. During the 720s, the Khazars transferred their capital to Samandar, a coastal town in the north Caucasus noted for its beautiful gardens and vineyards. In 750, the capital was moved to the city of Itil (Atil) on the edge of the Volga River. In fact, the name "Itil" also designated the Volga River in the medieval age. Itil would remain the Khazar capital for at least another 200 years. Itil, the administrative center of the Khazar kingdom, was located adjacent to Khazaran, a major trading center. In the early 10th century, Khazaran-Itil's population was composed mostly of Muslims and Jews, but a few Christians lived there also. The capital city had many mosques. The king's palace was located on an island nearby, which was surrounded by a brick wall. The Khazars stayed in their capital during the winter, but they lived in the surrounding steppe in the spring and summer to cultivate their crops.

The great capital city of modern Ukraine, Kiev, was founded by Khazars or Hungarians. Kiev is a Turkic place name (Küi = riverbank + ev = settlement). A community of Jewish Khazars lived in Kiev. Other towns of the Khazars, many of which also had important Jewish communities, included Kerch (Bospor), Feodosia, Tamatarkha (Tmutorokan), Chufut-Kale, Sudak, and Sarkel. The local governor of Samandar was Jewish, and it may be assumed that many of the governors of these other localities were also Jewish. A major brick fortress was built in 834 in Sarkel, along the Don River. It was a cooperative Byzantine-Khazar venture, and Petronas Kamateros, a Greek, served as chief engineer during the construction.

Civilization and trade. The staple foods for the Khazars were rice and fish. Barley, wheat, melons, hemp, and cucumbers were also harvested in Khazaria. There were many orchards and fertile regions around the Volga River, which the Khazars depended upon due to the infrequency of rain. The Khazars hunted foxes, rabbits, and beavers to supply the large demand for furs.

Khazaria was an important trade route connecting Asia and Europe. For example, the "Silk Road" was an important link between China, Central Asia, and Europe. Among the things traded along the Khazar trade routes were silks, furs, candlewax, honey, jewelry, silverware, coins, and spices.Jewish Radhanite traders of Persia passed thru Itil on their way to western Europe, China, and other locations. The Iranian Sogdians also made use of the Silk Road trade, and their language and runic letters became popular among the Turks. Khazars traded with the people of Khwarizm (northwest Uzbekistan) and Volga Bulgharia and also with port cities in Azerbaijan and Persia.

The Khazars' dual-monarchy was a Turkic system under which the kagan was the supreme king and the bek was the civilian army leader. The kagans were part of the Turkic Asena ruling family that had provided kagans for other Central Asian nations in the early medieval period. The Khazar kagans had relations with the rulers of the Byzantines, Abkhazians, Hungarians, and Armenians. To some extent, the Khazarian kings influenced the religion of the Khazar people, but they tolerated those who had different religions than their own, so that even when these kings adopted Judaism they still let Greek Christians, pagan Slavs, and Muslim Iranians live in their domains. In the capital city, the Khazars established a supreme court composed of 7 members, and every religion was represented on this judicial panel (according to one contemporary Arab chronicle, the Khazars were judged according to the Torah, while the other tribes were judged according to other laws).

Ancient communities of Jews existed in the Crimean Peninsula, a fact proven by much archaeological evidence. It is significant that the Crimea came under the control of the Khazars. The Crimean Jewish communities were later supplemented by refugee Jews fleeing the Mazdaq rebellion in Persia, the persecutions of Byzantine emperors Leo III and Romanus I Lecapenus, and for a variety of other reasons. Jews came to Khazaria from modern-day Uzbekistan, Armenia, Hungary, Syria, Turkey, Iraq, and many other places, as documented by al-Masudi, the Schechter Letter, Saadiah Gaon, and other accounts. The Arabic writer Dimashqi wrote that these refugee Jews offered their religion to the Khazar Turks and that the Khazars "found it better than their own and accepted it". The Jewish Radhanite traders may have also influenced the conversion. Adopting Judaism was perhaps also a symbol of political independence for Khazaria, holding the balance of power between Muslim Caliphate and the Christian Byzantine Empire.

Under the leadership of kings Bulan and Obadiah, the standard rabbinical form of the Jewish religion spread among the Khazars. King Bulan adopted Judaism in approximately the year 838, after supposedly holding a debate between representatives of the Jewish, Christian, and Muslim faiths. The Khazar nobility and many of the common people also became Jews. King Obadiah later established synagogues and Jewish schools in Khazaria. The books of the Mishnah, Talmud, and Torah thus became important to many Khazars. Saint Cyril came to Khazaria in 860 in a Byzantine attempt to convert the Khazars to Christianity, but he was unsuccessful in converting them away from Judaism. He did, however, convince many of the Slavs to adopt Christianity. By the 10th century, the Khazars wrote using Hebrew letters. The major Khazar Jewish documents from that period were written in the Hebrew language. The Ukrainian professor Omeljan Pritsak estimated that there were as many as 30,000 Jews in Khazaria by the 10th century. In 2002, the Swedish numismatist Gert Rispling discovered a Khazar Jewish coin.

In general, the Khazars may be described as a productive and tolerant people, in contact with much of the rest of the world and providing goods and services at home and abroad. Many artifacts from the Khazars, exhibiting their artistic and industrial talents, have survived to the present day.

Decline and fall. During the 10th century, the East Slavs were united under Scandinavian overlordship. A new nation, Kievan Rus, was formed by Prince Oleg. Just as the Khazars had left their mark on other peoples, so too did they influence the Rus. The Rus and the Hungarians both adopted the dual-kingship system of the Khazars. The Rus princes even borrowed the title kagan. Archaeologists recovered a variety of Khazar or Khazar-style objects (including clothing and pottery) from Viking gravesites in Chernigov, Gnezdovo, Kiev, and even Birka (Sweden). The residents of Kievan Rus patterned their legal procedures after the Khazars. In addition, some Khazar words became part of the old East Slavic language: for example, bogatyr ("brave knight") apparently derives from the Khazar word baghatur.

The Rus inherited most of the former Khazar lands in the late 10th century and early 11th century. One of the most devastating defeats came in 965, when Rus Prince Svyatoslav conquered the Khazar fortress of Sarkel. It is believed that he conquered Itil two years later, after which he campaigned in the Balkans. Despite the loss of their nation, the Khazar people did not disappear. Many of them converted to Islam and survived in the North Caucasus and Central Asian regions under new identities. Others lived and studied in other Jewish communities from Spain to the Byzantine Empire2 but in the end had no impact on the ancestral composition of any modern Jewish population.

Notes.

"The Khazar people were an unusual phenomenon for Medieval times. Surrounded by savage and nomadic tribes, they had all the advantages of the developed countries: structured government, vast and prosperous trading, and a permanent army. At the time, when great fanatism and deep ignorance contested their dominion over Western Europe, the Khazar state was famous for its justice and tolerance. People persecuted for their faiths flocked into Khazaria from everywhere. As a glistening star it shone brightly on the gloomy horizon of Europe, and faded away without leaving any traces of existence."  - Vasilii V. Grigoriev, in his essay "O dvoystvennosti verkhovnoy vlasti u khazarov" (1835), reprinted in his 1876 compilation book Rossiya i Aziya on page 66

"Though the Jews were everywhere a subject people, and in much of the world persecuted as well, Khazaria was the one place in the medieval world where the Jews actually were their own masters.... To the oppressed Jews of the world, the Khazars were a source of pride and hope, for their existence seemed to prove that God had not completely abandoned His people."- Raymond Scheindlin, in The Chronicles of the Jewish People (1996)

         1. Many medieval writers attested to the Khazars' Turkic origins including Theophanes, al-Masudi, Rabbi Yehudah ben Barzillai, Martinus Oppaviensis, and the anonymous authors of the Georgian Chronicle and Chinese chronicle T'ang-shu. The Arabic writer al-Masudi in Kitab at-Tanbih wrote: "...the Khazars... are a tribe of the Turks." (cited in Peter Golden, Khazar Studies, pp. 57-58). T'ang-shu reads: "K'o-sa [Khazars]... belong to the stock of the Turks." (cited in Peter Golden, Khazar Studies, p. 58). In his Chronographia, Theophanes wrote: "During his [Byzantine emperor Heraclius] stay there [in Lazica], he invited the eastern Turks, who are called Chazars, to become his allies." (cited in Theophanes, The Chronicle of Theophanes Confessor, translated by Cyril Mango and Roger Scott, 1997, p. 446). The claim that the Khazars were Scythians is completely without merit.
         2. Timothy Miller discovered that Jewish Khazars were members of the Jewish community of Pera in the Byzantine Empire around the 11th century (see Timothy S. Miller, "The Legend of Saint Zotikos According to Constantine Akropolites," Analecta Bollandiana vol. 112, 1994, pp. 339-376).

Suggestions for further research. Here are some useful published introductory materials on the Khazars. Some are available from retail bookstores, while others are only available through libraries.

“The Jews of Khazaria” by Kevin Alan Brook (2018). 10 chapters, plus glossary, timeline, bibliography, maps, notes. 

“The World of the Khazars edited by Peter B. Golden, Haggai Ben-Shammai, and András Róna-Tas (2007)

“Khazarian Hebrew doments of the Tenth Century by Norman Golb and Omeljan Pritsak (1982). .

“The History of the Jewish Khazars” by Douglas M. Dunlop (1954, 1967)

"Khazar Studies: An Historico-Philological Inquiry into the Origins of the Khazars" by Peter B. Golden (1980)

Journal article "Khazaria and Judaism" by P.B.Golden, in Archivum Eurasiae Medii Aevi, volume 3, 1983, pages 128 to 156.

“The Kuzari: in Defense of the Despised Faith by Yehudah HaLevi, translated by N. Daniel Korobkin (1998, 2009)

From:

http://www.khazaria.com/khazar-history.html