If a father has no rights to his child can I still get child support?

If your child's father's parental rights were terminated, he has no responsibility to pay child support.

If his parental rights have been terminated you cannot get child support from him.

If the father's rights were terminated by a court, his financial obligations were probably also terminated. But, a definite answer can only be provided by the child protective services' attorney who handled the termination. The order of termination should specifically say what the law of your state requires.