This niggun is from the city of Nevel. The chosid Reb Shlomo Der Geller (the Melamed of Nevel) used to sing is a lot.
Reb Yosel Reizes relates:
I remember how on Simchas Torah 5734 (1973), the Rebbe began the niggun "HaAderes V'haEmuna" to the tune of the French national anthem. But first as an introduction - the night of Shemini Atzeres, in the middle of the Hakafos, the Rebbe took the siddur and went to the edge of the platform. Everyone became quiet, to hear what the Rebbe would say and then the Rebbe began to say the pesukim of the fourth hakafa to the tune of the traditional "HaAderes V'haEmuna" which is also known as the "HaAderes V'haEmuna of Nevel."
The Rebbe said a pasuk and everyone answered "Tchai olamim." The Rebbe continued until he came to the end of the pesukim of the Hakafa, saying the words "ne'imos b'yemincha netzach" very loudly.