Jeese... does ANYONE know how to use the search function at the top of the screen.

It's a human Child... not a car. That's been asked and answered say... about 15,000 times. With the very same answer every time.

Are you the father or the mother ?

No the father can not just sign his rights away, if it was that easy there would not be 100,000 fathers in jail right now for failure to pay child support.

If there is a new step parent willing to adopt, then they may sign away the rights to allow the adoption.

https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html