Are you definite you are the biological father?... What contact/relationship do you have with the child?.... The law sees both biological parents as responsible for a child, financially & otherwise... There is no legal way to remove that responsibility except by adoption
Yeah, as Atticus said, I guess the only way to 'hand over parental responsibility' is to prove you aren't the father with a DNA test. But if you are, there isn't anything you can do that I'm aware of.