Joint custody

Well if you already have joint custody then the father will not be able to modifly that order,unless he can prove the child is in danger by being with you, if you have never filed for custody of your child, and the father is in the childs birth certificate then he can ask for joint custody, but because you were never married chances are slim of him being able to. Just because parents are awarded joint custody does not mean that there is no child support order to be enforced, child support is based on more than 50/50 custody, it is based on the income of both parents, day care, health insurance (If Any) and other factors so if he is banking on getting out of child support on this one he will be in for a surprize it he does file a motion, if he is not on the childs birth certifiacte then he has no rights until he takes a DNA, then he can file for visitation.

His Child support should not change. It really has nothing to do with custody and only to do with parental income and expenses of raising a child. He "could" sue you for child support if he took you to court and was awarded "physical" custody of the child... but this is highly unlikely unless he can prove the child is in danger and would be better off with him.