We do know that they were not a significant contributor to the genetic ancestry of Ashkenazi Jews, so wherever they went, they were probably very small in numbers. It’s likely that many simply assimilated into later groups moving through their former territory.

However, what happened to the Jewish Khazars is a different story. They may have been so small a group within the aristocracy that they ceased to exist. Small numbers of them may have also joined other Eastern European Jewish groups, for example the East Slavic speaking Jews of Brest and Grodno…

There isn’t any one group you could point to and say “they are descendant from the Khazars.” There are scattered references to Khazars fleeing the destruction of the Khaganate. For example, one group appeared to convert to Islam and move to Azerbaijan, then-ruled by an Islamic Khazar official…

“At the present time we know of no nation under the heavens where Christians do not live. For Christians are even found in the lands of Gog and Magog -- who are a Hunnic race and are called Gazari. They are circumcised and observing all the laws of Judaism.”

Christian of Stavelot, writing in the late 8th or early 9th centuries in Francia, reported his knowledge of Khazar Judaism:

for a variety of reasons, including the Khazar Correspondence where King Joseph reported that one of the Bulanids was named "Hanukkah." There are some other pieces of textual evidence, but the lived, day-to-day Judaism of the Khazars will most likely remain unknown.

Unfortunately, we will probably never know for sure. Besides scattered references to the Khazars inviting foreign Jewish sages to establish 'proper' Judaism in the country, we know very little about what form the religion took. Historians are pretty sure it leaned Rabbinical and not Karaite...

Firkovich is a bigger issue where it concerns the exact form of Khazar Judaism since he was accused of fabricating evidence to support the Khazars as Karaite. "The World of the Khazars" I mentioned earlier has a section by Artem Fedorchuk about this topic.

Admittedly, I am among those who rarely engage with the historians who deny the authenticity of the Cairo Genizah documents, and I'm having a hard time digging through my notes to find out exactly where the issue comes from. The reply by @theophite.bsky.social might explain more than I can.

Of course saying this is a bit like argumentum ad populum, although it's hard to go into more detail because most mainstream Khazar historical writing I am aware of barely engages with those who reject the authenticity of the Cairo Genizah documents. The same is true vice versa.

A vast majority of mainstream Khazar scholars regard it as legitimate, most notably Peter Golden (see The World of the Khazars 2007). There is a much smaller school of historians who dispute it and other Khazar-related documents found in the Cairo Genizah, but they are not in the majority.

There is only one recorded word known today which was most likely written in the original Khazar language: “[H]oqurüm,” meaning something like “I have read it.” It was written in Turkic runes at the end of the Kievan Letter, which was otherwise written in Hebrew. #history

During the era of the Khazars, a new material culture developed around their territories near the Dnieper and Don rivers. This culture is referred to as the Saltovo-Mayaki culture by historians. It may have represented a multiethnic mix of Turkic, Finnic, Iranic, and Slavic populations. #history

Thus, there is no real consensus on whether this constitutes a community of Kabars, some of whom were Jewish, Jews of a different group such as the Avars, or a mix of Khazar and non-Khazar graves, among other possibilities. #history

Magyar migration to Pannonia. They contain numerous artifacts from a Central Asian group, interspersed among Jewish symbols and artifacts such as menorahs, shofars, and Hebrew inscriptions. Some of the (apparently non-Jewish) graves demonstrated pagan burial practices, such as horse sacrifices...

Scholars are interested in whether any Kabars were Jewish, although there is no conclusive evidence that proves that fact. The most interesting evidence is the Chelarevo burial finds in Vojvodina, Serbia. The graves at this site date back to the 10th century, around the time of the...

When the Magyars migrated west into Pannonia, they were joined by a group of Khazars, potentially rebels, known as the Kabars. The Kabars participated in the Magyar raids throughout Europe and settled alongside the Magyars in Hungary.

One of the only pieces of physical evidence of Khazar Judaism is the Moses Coin, a Khazar copy of an Islamic silver Dirham which subtly changed the Shahadah to read "Moses is the messenger of God." The Moses Coin was found as part of the Spillings Hoard in Gotland, Sweden. #history

Source: "Coup d'état, Coronation and Conversion: Some Reflections on the Adoption of Judaism by the Khazar Khaganate" by J. T. Olsson. #history

the public, the aristocracy, or the Bek. The latter two may have used this as a sort of pressure valve to control unrest and deflect blame for their own failures. Some theories about the rise of Bulan see him as a Bek using one such time of crisis to launch a coup against the Khagan.

The Khazar Khagan may have been a sacrificial figure. Like other rulers from throughout Eurasia, they were expected to maintain something of a “mandate of heaven,” and if they failed to do so after military defeats, ecological disasters, or other setbacks, they could be killed by…

We will likely never know the total truth of the Khazar conversion. The aristocracy most likely converted, but the extent to which Judaism existed among the general population of the Khaganate is not clear. #history

Modern theories range from converting to Judaism as a counter to the imperial ambitions of the Byzantine Empire and the Islamic Caliphates in the aftermath of the Second Arab-Khazar War, to Bulan being descendant from Byzantine-Jewish refugees and instituting the religion after a coup...

They would choose if they couldn't choose their own. The Christian and the Muslim, being constantly at war in Byzantium and the Islamic Caliphate, both chose Judaism. And so Bulan converted to Judaism and called on scholars from Babylon to help establish the religion in the country...

The traditional Khazar account from the Khazar Correspondence has Bulan as a non-conforming monotheist who called Christian, Muslim, and Jewish religious leaders to his court to help decide which Abrahamic religion he would convert to. After days of debates, he asked each official which religion...

The first Jewish Khazar ruler was a man named Bulan, or Sabriel. It's not currently known whether he was Khagan or Bek, although most historians suspect the latter due to his role within the Khazar military. There are multiple accounts of his decision to convert to Judaism...

Khazaria was home to Jews of numerous backgrounds: The ancient Jewish communities of Crimea, the Mountain Jews in the Caucasus, Greco-Jewish refugees who fled the Byzantine Empire, and Radhanite merchants who ranged throughout Eurasia, to name the largest groups. #history

According to De Administrando Imperio by Byzantine Emperor Constantine VII, it was the Khazar Khagan who suggested the Magyars select a single ruler from among their tribal confederation. That ruler was Álmos, whose son and successor Árpád founded Hungary’s first medieval monarchy. #history

The Khazars extracted tribute from numerous neighboring groups, including the Severians and Radimichians, Bulgars, Alans, Burtas, Magyars, and various Finno-Ugric peoples living in the forests to their north. Furs were often taken as tribute, which the Khazars traded with the Arabs. #history

The Khazars most likely had a system of dual kingship similar to other early Turkic groups: The Khagan was the supreme spiritual leader, and the Bek (or Khagan Bek) was the main political and military ruler. #history