The fighter is defending in the air, so it will not be trapped. In fact, it will not be able to land and must find another landing spot within one space or be lost.
The only way that a plane can be trapped on a carrier is if the carrier is attacking and the plane belongs to an ally. Since it is not the ally’s turn, the plane remains on the carrier as cargo during the attack, and will be trapped if the carrier is damaged. In such a case, if the carrier is attacked while still damaged, the trapped plane will be unable to leave the ship, and thus unable to participate in the battle. It will be lost if the carrier is sunk.