Can i refuse visits til my daughter is older?

I would feel the same way as you do! I am from the US so i don't know exactly how much he pays in child support! In most states here if he pays child support he has right to visitations, but im sure you could get them supervised. I would talk to a social worker and see what your right are. I would go to court and FIGHT FIGHT FIGHT! I have a friend here and she and her boyfriend broke up a couple years after she had her daughter but anyways she had all the evidence that her ex molested her daughter but she still had to see her dad on weekends and eventually he got custody of her daughter because he claimed that he never did anything to her and that she was making up all these lies. I mean her daughter who was 2 at the time told her mom that Daddy made me put his thing in my mouth there was way more to go along with the evidence but I guess here in the US you can get away with anything!