The father of my unborn child has....?

been back and forth first "acting" supportive-then disappearing with another woman for a few months of my pregnancy and then reappearing "wanting to be a part of babies & my life" only to once again have the other woman "in" and me&baby "out" - I am done with his games but I don't want the baby to grow up without a father -I also can not afford to raise the child on my own -with no financial istance. If I name the father on the birth certificate-then file for istance- the state will "go after" him for child support which he can not pay- and he will go to jail so either way my baby will not have his father- I am so confused - and hurt...should I just try to raise the baby with no contact with the father or should I live a life of misery trying to deal with him for the babies sake?