I highly doubt he'd ever get visitation with a history like that and the fact he's never been around your son. How old is your little boy?
Talk to a lawyer. If he is going to take you to court, you need legal advice. (You can bet he will have it. If he even follows through with his threat.)
If you are getting child support from him he has rights to his child. If you don't want him to be around your kid you will have to give up getting child support. You can't change who his dad is.
The only way to prevent him seeing the kid is if you can prove he's a physical danger to him. As in hurt him or did something like drink and drive with his son in the car.
If you an your fiance get married, you can go to court and try to get his rights terminated and have him adopted by your fiancé.
Unless there is a extreme physical or mental danger to the child, courts are reluctant to terminate bio rights. Rights you gave him with that DNA test and child support order. Has he paid for any financial support for your child?