My child is 5months and she has my last name, and her dad isn't on her birth certificate. He wasn't around during my pregnancy and he decided not to be on her birth certificate. He would come around after she was born and for the past 4 1/2 months he was buying formula and diapers. But then out of nowhere he decided he didn't want to be around me or her and he stopped buying her stuff. But yet he tells me he is going to fight for full custody? Is that possible?

Sure he can fight for full custody but he'll not get it unless you are an unfit mother and he proves it to a judge in court. He may get visitation, maybe even joint custody but your story will go a long way againist him in court. Are there more details you can tell us.

Unless his name appears on your child's B.C. he had no claim to her nor does he have any perental rights, he can try to get custody but its highly unlikely he will unless he can prove you to be an unfit mother. I don't think you need to worry he's probably just wanting to get at you.

Positive parent is not telling you the entire story,

First he will have to file in court for a DNA test to prove he is the father. After that while he can go for full custody, most likely he will go after joint custody which is very common among parents today, so yes he has a very good chance at that.

At the least he will get visits. A couple weekends a month that he takes the child, perhaps a night during the week or every other week also. And a few weeks at the summer, is almost a min they give if there is no threat from his with child.

So you will not stop him seeing and being part of the child's life.

And he owes you nothing, at this point, you have not filed for child support, so he has no legal obligation to pay you anything.
So his not paying can not be used against him, since he does not owe it