What can he do, if anything, and what are his rights if the child is not biologically his?

Your story has big gaping holes in it. It does not make a whole lot of sense and as you have told it, your daughter is most likely in no condition nor is she fit to have custody of a child. So why you want the child back is questionable. Seems very likely the child would be in just as much danger or more in your daughters care as in the care of the person who has the child now. First, no where in America can a woman 'sign over a child' like its a piece of property, especially just after giving birth, under the influence of drugs and in the care of a hospital. Second, if she did, she can't later say oops, I've changed my mind and unilaterally 'rescind the agreement'. Third, your daughter's mental state is very suspect, if she after all that, allowed him to 'talk her into' taking the child to NC. However, if he is not the father, he has no rights. Why you aren't down in NC with a court order and a couple of sheriff's deputies to take custody of the child is beyond me. I suspect it is because while a DNA test may have been ordered by a NJ court, if I were him in NC, I'd flip NJ the bird, completely blow them off and not take the test. So most likely, you do not have DNA evidence that he is not the father. Besides if you did, why would he want to keep the child? What you need to do is get on the ball and get a court order asap. As for his big 'next step', there isn't a legal one in NC because he doesn't have jurisdiction. However, there are plenty of illegal next steps. If he really is not the child's father, I'd be concerned the child will be sold either to an illegal adoption agency or to human traffickers. If that happens, you have about a 48 hour window before you'll most likely never see that child again.