I don't think so, but I'd be pretty interested if hey did. Chess.com has over 100,000 puzzles...
I think it would look something like this:
1. Mate in ones
2. gain material
3. Fork
4. exploiting pins
Less (or the least, as I know it, because I've only done like 4 of each even after doing 15,000 puzzles) common would be the 2 Bishops Mates and Alekhine's gun.

And if there is not such a list, how do you think a top list would look like?
1. Pin
2. Fork
3. ?
4.
Not easy to measure accurately I think. But that is not my question.