If a ball is hit in fair play bounces foul but is caught in the air in foul territory is it fair or foul?

Your question is difficult to understand because of the way it is worded, so I'll try and cover the whole fair/foul question.

Any caught fly ball is an out, regardless of whether the ball is in fair or foul territory when caught, unless it is caught in out-of-play territory, in which case it is just a foul ball.

Any ground ball that is first touched while the ball is in fair territory is a playable fair ball, regardless of what happens after the touch, unless and until it goes into out-of-play territory.

Any ground ball that is first touched while the ball is in foul territory is a foul ball, regardless of what happens after the touch; if it is never touched, it is a foul ball.