Trying to find out if a parent has to pay a fee for giving up their parental rights in the state of Wisconsin

Have you read this "sticky" thread (https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html)?

So no, If the child is being adopted, is doubtful that the biological parent would be asked to pay a fee in order to consent to such adoption.

You are assuming a parent CAN give up their parental rights. That is a faulty assumption.