I have raised my son all by myself since he was born. The father has wanted nothing to do with me or my son since I found out I was pregnant. He refused his paternity test and now doesn't want to pay $373.00 a month that CSE is asking. He now is wanting custody. I tried dropping the case because I don't want my child around him or his fiancé because of they're criminal history and other reasons. But now the attorney doesn't want to dismiss it at this time. What do I need to do?

I have raised my son all by myself since he was born. The father has wanted nothing to do with me or my son since I found out I was pregnant. He refused his paternity test and now doesnt want to pay $373.00 a month that CSE is asking. He now is wanting custody. I tried dropping the case becasue I dont want my child around him or his fiance because of theyre criminal history and other reasons. But now the attorney doesnt want to dismiss it at this time. What do I need to do?

Let me remind you my son is almost 9 months old and has only been around this guy 10 minutes only 3 weeks ago.

Father even after years has legal rights to ask for custody, or joint custody or visits.

This is obvious retaliation for asking for child support and is a normal and almost expected threat. You defend the motion, showing that there is no reason for custody to be changed.
You also make sure child support is set at proper levels if that is not already done.

If you applied for public assistance, then the state will want him to pay support rather than use taxpayer money. So you can't drop this. If he refuses a court ordered paternity test, he can be held in contempt of court. Or the court will assume he's refusing because he knows he is the father.

It takes a lot to take a child from its mother, but he is likely to get visitation. But, I suspect, if it won't reduce his support obligation he won't bother.

But you chose to have sex with this man. That choice had consequences and this is one of them.