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Here is the description, which should give you more details:

Tzadikite, meaning "righteous one", represents the mystical and Kabbalistic form of Judaism practiced mainly by the Juhuri people in the Caucasian Mountains. Highly militaristic, this form of Judaism is centered on martial prowess and skill.
 
https://en.wikipedia.org/wiki/Mountain_Jews#Religion

Mountain Jews are neither Sephardim (from the Iberian Peninsula) nor Ashkenazim (from Germany and Eastern-Europe) but rather of Persian origin. Mountain Jews tenaciously held to their religion throughout the centuries, developing their own unique traditions and religious practices.[37] Mountain Jewish traditions are infused with teachings of Kabbalah and Jewish mysticism.

So it seems to be a heresy to differentiate the Caucasus Jewish practices from other Judaic people. Tzadik Nistarim is a belief based in Kabbalah so I'd imagine the name is still a reference to Tzadikim in some regard.