Can I request supervised visitation if my chilld's father is not fit?

I left my son's father in October, after the police were called for a domestic situation. He has an anger problem. I have seen how he treated our son while living with him and how he has cared for his daughter from a previous relationship. I have my son at all times. I have never denied the father of seeing his son. I just asked could he come visit with him in my city so I can see their interaction. Then I would think about letting go there. He only wants to see him at his home. His home is unfit. He doesn't want to do anything for the child unless he's at his home. He does send money but told me if he didn't send the money he could start coming to see him in my city. I told him to stop but he says he doesn't want to see him here. So he doesn't want to support financial or see him unless it's in his home.