Relinquished has an effect that says can only be used once per turn... Does mean Player A use on turn?

You're right to ask! The wording on "once per turn" effects in Yu-Gi-Oh! can be a little tricky. Here's the breakdown:

"Once per turn" means the effect can only be used once during that player's turn**, regardless of how many times they activate it.

So, to answer your question:

* Player A can use "Relinquished"'s effect once during their turn.

* Player B can also use "Relinquished"'s effect once during their turn.

It's important to note:

* The "once per turn" restriction applies to the player's turn, not the entire game.

* It does not prevent the effect from being used again in a subsequent turn.

I hope this helps clarify!