Hey Private User, nice to meet you here too. ;-)
I've just merged 2 profiles then noticed this discussion.
This is actually the earliest clue I have of Kanner/ Kanir being kohanim.
I'm yet to find how and if this is the same Kanner which is my Shver's Private 3rd-great-grandfather.
I gleaned this information from the following interactive trees on JewishGen
https://www.jewishgen.org/webtrees/individual.php?pid=I144&ged=...
and matching Jacob Zvi to this tree
https://www.jewishgen.org/webtrees/individual.php?pid=I04991&ge...
which traces back to the Chacham Zvi.
I've tried finding this lineage in Geni but in the descents of the Chacham Tzvi Hirsch Ashkenazi I couldn't trace the above beyond his son R' Ephraim Ashkenazi of Lwow (s#6). And there isn't any information here about the ancestors of Yackov Zvi Kanir.
Were the parents of Jacob Zvi, Meir Kanir & Esther Etil Ashkenazi? Was Jacob Zvi a brother of Chaim Efraim Efroyim Kanner?
We have b'msorah in the family that the Kanner's were descendants of the Chacham Zvi. Is this the lineage?
Best regards
Shragi Leitner
PS. Private User I know you only live around the corner, but sorry I have no clue who you are. Who is your father?