Ok so some friends and I were playing a 7 player game of heroclix. One player was using Frankencastle and he used his drill drone gun on another player. Thats when the debate began on how it would work in our game. Here is what the power states:
DRILL-DRONE GUN: When Franken-Castle hits a character with a ranged combat attack, you may choose to deal no damage and mark that character. Even if this power is countered or lost, at the beginning of each of your turns deal 1 penetrating damage to each marked character. Marked characters may be given a double power action to remove the mark.
So what we were wondering is if at the beginning of every single players turn would the hit character take a click? Or at the beginning of only the attacker and hit characters turn. I thought it was at the beginning of every turn but who knows. Any info would be helpful, thank you.

It says at the begining of each of your turns, not at the beginning of each turn. It should be applied at the start of the turn for the player who is controlling Frankencastle.

"Each of your turns" refers to the player using Frank. Otherwise, it would read something like "at the beginning of each turn."

I'm going to say these 2 know what they are talking about.... This activates on your turn.

Got ya. Thanks you guys.