Petition for a paternity test

The man on my daughter's birth certificate is trying to take her away from me and have me pay him child support. I recently had a DNA test performed and can prove that he isn't the biological father, but he has been on her birth certificate longer than two years. I wasn't able to petition for one before due to him being incarcerated the majority of my daughter's life. She has no emotional bond or connection with him at all. I am wanting to petition for the court to finally give them a DNA test and can prove that I allowed him to sign the birth certificate under duress because we were in a severely physically abusive relationship before my daughter was conceived and I will very afraid of him.