Is it that he doesn't want to pay for the paternity test, or he doesn't want to pay for child support? In my state, since I was on Medicaid for pregnant women, if the father wanted a paternity test - he had to pay and they would bill him, so it wouldn't be my problem. However, if it's child support that he doesn't want to pay -- the courts can order it, but that won't make him pay. If he's trying to get full-custody and you want to fight that, then you need to get a lawyer to help you make your case.