I believe this a "dotted" edge variety of 10 kopeks 1861. Many books mark this variety
as rare. Have you any idea exactly how rare it is? (Or is this the rare variety at all?)

i would have a clue i dont have any kopeks in my collection but with the edge dotted like that wouldnt it be easy to just stamp the edge???

Paris Mint ?

its st petersburg mint not paris

I believe It's Paris mint (no mintmaster's mark)

Mint mark and mintmaster initials are two different things -- there is С.П.Б on the reverse, so no doubt about it being St. Petersburg mint.

There's is С.П.Б in every variety. No minmaster's mark shows it was stuck in France (Paris or Strasbourgh according to Uzdenikov). Correct me if I'm wrong. Only 1915-17 there's is no mintmark.

You are right, janneen -- I wasn't aware of that! Sorry for the confusion ...
R.W. Julian, on page 25 of his book "Russian Silver Coinage 1796-1917", mentions that edge variety No. 2 (for 10 kopeek coins of 1860-1866) has several variations. I assume that one of these would be the edge you have shown. However, he doesn't list the 1861 French strike as being scarce (1861-МИ is rare, according to him -- I didn't look anywhere else since I don't actively collect this series). It is entirely possible that variety collectors might consider this particular edge variety as scarce, though.

I think it's listed in Konros. ($30 in VF). I'm not quite sure because it's in russian.
It's also Uzdenikov nr. 1801.