You are 100% correct regarding Checyians who were and are referred to as Mountain Jews. Here is a bit more info and a site to verify these extracted facs from:
Mountain Jews - Wikipedia, the free encyclopedia
In Chechnya, the Jews became notably well-integrated into Chechen society. A clan, Dzugtoi, was formed for Chechen Jews long ago, perhaps
during the Middle Ages.
In Chechen culture, there is an assembly of clans (taips). Of the total 90, 20 were originally founded by foreigners (a new taip can be founded at any time as long as there is a considerable founding group).[2]
In founding the new taip, its members pledged eternal loyalty to the Chechen nation, and hence became part of the nation, being simultaneously Chechens and Jews (there are also Polish, Russian, Armenian, Georgian, Turkish and other clans).[2][3]
Over time they become more and more integrated, due both to assimilation and to the Chechen populace becoming used to their presence. Interclan marriages were common, so eventually they became largely indistinguishable from other Chechens, except for their faith.[2][3] The original Mountain Jews of Chechnya now speak mostly Chechen.[4]
Some historians believe that the Jews also influenced Chechen culture.[5][6]
Many common Chechen names usually attributed to Arabic origin, due to their Semitic roots, have been shown to have existed before the Islamization of Chechnya.
According to Andrey Zelev, many Chechen place names show Jewish influence.
The Georgian historian Leonti Mroveli, who considers the Khazars a people closely related to the Chechens, and Ruslan Khasbulatov, who stated that Chechens are 30% Jewish, also support the idea of Jewish influence.
Their theories are controversial, and have not achieved widespread acceptance.[7]
Mountain Jewish men, c. 1900 (1905-06 Jewish Encyclopedia)
History also records the large number of Jews in Babylonian Captivity in what is today Iran. About 25,000-40,000 Jews remain in Iran today, 2011.
Many old Babylonia Jews crossed from Iran/Babylonia/Ottoman Empite of old into what we today know as Checynia between the 5th and 7th centuries AD. Please do some Internet searches and satisfy yourself. Thanks.