We discussed the Mountain Jews and their language, Juhuri (Judeo-Tat), back in 2010; now you can see glorious photos of the place where they speak it and read an account of meeting its speakers at Poemas del río Wang:
I met Mountain Jews for for the first time seven years ago, in a café of the Tabriz bazaar, where I was listening to the conversation of the waiters. The language was particularly familiar, some Iranian language, but not Persian, and not even Kurdish. “In what language do you speak?” I asked. “Be Juhuri, in Jewish”, they answered. “Come on”, I said, “I know two Jewish languages, but neither of them sounds like this.” “Well, this is then the third one. We, Mountain Jews speak in this language.” And they said that thousands of them live in the mountains of the “other”, northern, Azerbaijan, and farther north, in Dagestan, many more still.
Take the stuff about the Babylonian captivity with several spoonfuls of salt; as Etienne says in that 2010 post, “the notion that Judeo-Tat goes back to Persian acquired by Jews in the days of King Nebuchadnezzar is utter nonsense. From what little I know of Tat, it is clearly so similar to Modern Persian that it cannot have broken off from Persian at such an early date.” Otherwise, it’s an amazing account:
The most unusual fact about this shtetl is that it works. Anyone who has seen the deserted houses of the Galician shtetls and the Jewish streets of the Eastern European villages, the closed down synagogues or their empty places, and brought them to life again in the imagination with the characters of Sholem Aleichem, can see here how that world would look, had its inhabitants not disappeared. The traditional Jewish world of the Red Shtetl has only gradually modernized. The town center has been renovated, but they have also built a new mikve, a kosher butcher’s shop, and a community house called “The House of Happiness”, and the facades of the ostentatious palaces built in the places of the old wooden houses are still decorated with the motifs of traditional Jewish iconography.