If a card is attached to my character can i pay its cost to move it to an other characther or only the player who played the attachment can use its skill?

Panugeta said:

You may want to clarify your question with an example.

The attachment I think you are referencing is Poisoned Wine which allows its controller to kneel 1 influence to attach it to another character.

What do you mean by "skill"? The bold text "Any Phase", "Response", "Challenges", etc? Or do you mean all of the text on the attachment?

The player who controls an attachment is the one who played it, until an effect changes that (all cards are controlled independantly). So if another player attaches something to one of your characters, you cannot use the attachment's text, because it is not yours.

That is why I wanted him to clarify what he meant by "skill". The attachment can have a passive effect which is in place regardless of who controls it. Example being "Attached character has -1 STR."

When the text is voluntary, like "Any phase" or "Response", only the controller can use that.

Thank you that's what i wanted to learn!

It's the same concept as characters, locations, etc. You cannot trigger the effects that are on characters and locations your opponent controls. So it makes sense that you cannot use your opponent's attachments, either. The tricky part for a lot of people is that control of attachments is determined by who played them, not by who controls whatever they are attached to.