Low income Medicaid application wants me to file for chid support to be able to receive benefits but I don't want my child's father to have any rights to my child she has my last name and he is not on the birth certificate due to being abusive on drugs and in and out of jail I need the benefits but I'm terrified he will get rights and my daughter doesn't deserve to have that in her life

You file for support and file for Full custody. Just because he pays support does not give him rights.

He already has rights because he fathered the child. Keeping him off the birth certificate doesn't change that. The only difference is he needs to go to court to enforce those rights. Whether you file for child support or not he can go to court and get some level of custody and visitation.

And, if you don't file against him for support then you will lose benefits and be depriving your daughter. Does she deserve that?

As to what rights he will have, that depends on whether you can prove he is a danger to her. Drug abuse and a criminal record can help. It may cause the courts to not allow visitation or give only supervised visitation. Bit one thing the court will look at, apparently this man was OK for you to have sex with, so how bad can he be? You chose to have sex with him and you and your daughter are going to have to deal with that decision for the rest of your lives.