My husbands name is on his ex wife's child's birth Certifacate. He is not the biological father. What can I do to remove his name so we can stop paying child support for a kid that is not ours?

Has a paternity test been done to prove he's not the father? Presumably your husband pays child support because there is a court order requiring him to - why didn't he contest his paternity of the child at that time? He should contact a lawyer to see about modifying that court order. Also - I assume that your husband never adopted the child, correct?