If you have a child born of rape, there are a number of states where paternity laws allow the father to sue for sole custody (unlikely) or joint custody (more likely, because it keeps them in contact with their victim as they arrange handoffs and custody arrangements).

There are also a number of states that allow the woman to try to sever paternity rights in cases of rape, but several of them require the perpetrator to be convicted of raping the victim, and there are (a couple? a few?) where the perpetrator has to be convicted of rape in the specific instance that led to the child (difficult in ongoing abuse cases).

Most states defer to the patriarchy, which is terrified of men “losing” the right to see their kids over vindictive, false rape claims.