I have a son that is four months old. I was never married to his father and have a No Contact Order and Civil Protection Order against him for violence during my pregnancy. I am moving out of state once my lease is up to be with family and better job opportunities. He is currently filing for Visitation/Custody and to remove my son from the Protection Order. The most he would ever be granted is Supervised Visitation. If he is granted Supervised Visitation does this mean that I can't move? Does it give him some kind of custody where I would be charged with kidnapping if I take my son anywhere?

If he is granted supervised visitation yes, you would need the permission of the court in order to modify that order. You may be allowed to move and return the child to a designated point for visitations. Its really up to the court to decide.

If he is awarded some kind of custody you could be charged with contempt if your move kept your ex from exercising is ordered visitation. If he was granted joint legal custody and you were to move hiding the child from him, yes, that can be prosecuted as parental kidnapping.