I have been court ordered to participate in a paternity test which I will do, however regardless of the results can I sign my rights over or away?

It is possible for you to file a petition seeking a court order terminating your parental rights. However, unless your child's mother has remarried and the husband is seeking to adopt your child, it is unlikely that a court would grant your petition. Since you have been ordered to participate in a paternity test, the mother likely wants you to pay child support. You cannot waive or sign away that obligation if you are the biological father. If you choose to not participate in your child's life, nobody can force to you be a father- but you CAN be forced to pay child support.