In most states, if the court orders it, you are stuck, no ands, ifs, or buts. And, to top it off, you have no right to the child as they will argue it isn’t yours.
https://www.legalzoom.com/articles/can-you-get-a-refund-if-the-child-you-support-isnt-really-yours
“If the law supposes that,” said Mr. Bumble, squeezing his hat emphatically in both hands, “the law is a ass — a idiot. If that’s the eye of the law, the law is a bachelor; and the worst I wish the law is, that his eye may be opened by experience — by experience.”
Charles Dickens
“Oliver Twist”