She is married and committed adultery

She is married to a man and left him and we messed around and she got pregnant. She later comes to me and says she wants me to take a paternity test even though they say they don't want me to be in the child's life they just want child support. By law will i have to pay child support anyway even if i dont ever get to see the child? Also can i just sign over my rights to her husband and not have to pay child support?