I am not really sure what your question is getting at. If he has not been determined by the court to be the father he has no rights that would "hold up" with law enforcement.
The reality is, if he wants to be designated father, then he needs to sign a paternity affidavit and register as father or seek a court action declaring him father. Either way without an order stating what his parenting time is, he has not rights.
If would be curious about what his motivation is and exactly what he wants you to sign as well as what he expects to accomplish from such a document.