Does putting a deadbeat on child support give him paternal rights?

Anonymous

I’m in Texas. Today I’m supposed to take my son to get a DNA test to prove my baby daddy is the father since I filed child support on him. Obviously my son is his so once the results come back does he get automatic rights to him?? I’m asking because he’s never even tried to meet his son. So I don’t think he deserves rights until he makes some kind of effort.