Mountain Jews are considered, by some, to be of Sephardic lineage; this however is a misnomer as they are neither Sephardim (from the Iberian Peninsula) nor Ashkenazim (from Germany and Eastern-Europe) but rather come directly by way of Persia. Mountain Jews tenaciously held to their religion throughout the centuries, developing their own unique traditions and religious practices. Mountain Jewish traditions are infused with teachings of Kabbalah and Jewish mysticism. Mountain Jews have traditionally maintained a two-tiered rabbinate, distinguishing between a rabbi and a "dayan." A "rabbi" was a title given to religious leaders performing the functions of liturgical preachers (maggids) and cantors (hazzans) in synagogues ("nimaz"), teachers in Jewish schools (cheders), and shochets. A Dayan was a chief rabbi of a town, presiding over beit dins and representing the highest religious authority for the town and nearby smaller settlements. Dayans were elected democratically by community leaders. The religious survival of the community was not without difficulties. In the prosperous days of Jewish Valley (roughly 1600-1800), the spiritual center of Mountain Jews centered on the settlement of Aba-Sava. Many works of religious significance were written in Aba-Sava. Here, Elisha ben Schmuel Ha-Katan wrote several of his piyyuts. Theologist Gerhson Lala ben Moshke Nakdi, who lived in Aba-Sava in 18th century, wrote a commentary to Mishneh Torah of Maimonides. Rabbi Mattathia ben Shmuel ha-Kohen wrote his kabbalistic essay Kol Hamevaser in Aba-Sava. With the brutal destruction of Aba-Sava (roughly 1800), however, the religious center of Mountain Jews moved to Derbent. Prominent rabbis of Mountain Jews in the nineteenth century included: Rabbi Gershom son of rabbi Reuven of Qirmizi Q@s@b@ Azerbaijan, Shalom ben Melek of Temir-Khan-Shura (modern Buynaksk), Chief Rabbi of Dagestan Jacob ben Isaac, and Rabbi Hizkiyahu ben Avraam of Nalchik, whose son Rabbi Nahamiil ben Hizkiyahu later played a crucial role in saving Nalchik's Jewish community from the Nazis. In the early decades of the Soviet Union, the government took steps to suppress religion. Thus, In the 1930s, the Soviet Union closed synagogues belonging to mountain Jews. Same procedures were implemented on other ethnicities and religions. Soviet authorities propagated the myth that Mountain Jews were not part of the world Jewish people at all, but rather members of Tat community that settled in the region. Soviet anti-Zionism rhetoric was intensified during Khrushchev's rule. Some of the synagogues were later reopened in the 40's. The closing of the synagogues in the 30's was part of communist ideology, which resisted religion of any kind. At the beginning of the 1950s, there were synagogues in all major Mountain Jewish communities. By 1966, reportedly six synagogues remained; some were confiscated by the Soviet authorities. While Mountain Jews observed the rituals of circumcision, marriage and burial, as well as Jewish holidays, other precepts of Jewish faith were observed less carefully. The community's ethnic identity remained unshaken despite the Soviet efforts. Cases of intermarriage with Muslims in Azerbaijan or Dagestan were rare as both groups practice endogamy. After the fall of the Soviet Union, Mountain Jews experienced a significant religious revival, with increasing religious observance by members of the younger generation.

Answer this question "Do they have any specific rituals related to this worship?" by extracting the answer from the text above.
While Mountain Jews observed the rituals of circumcision, marriage and burial, as well as Jewish holidays, other precepts of Jewish faith were observed less carefully.