Most states, including NJ, are first filed. Point being, law enforcement, judges, etc. are not family therapists, they are not in a position to decipher "who shot John" for lack of a better term (old fans of Dallas might get that reference).
Even if you have a situation where a child was fathered by a man who is already married, if he has older children through that marriage, most state guidelines do not even allow for those children to take precedence over the child who has been fathered out of wedlock. Even with the most die-cast prenup, that's a person-to-person contract, most states do not allow those to take precedence over state's presumption of responsibility.
Reason being: the state does not want to pay for that child, if that child were to ever end up on state aid of some form. The state presumes the father will either stay married or at least financially support the children he fathered within wedlock. Unless the wife files for divorce and requests
child support before a
paternity suit is filed, her children with her husband will be "next" in line, if a paternity suit is filed against him, thereby initiating the "first files first" process.
The only thing that absolves a man of this in NJ is a prenup. Even with a prenup, the wife will get set amount of agreed upon assets, but only after the child support obligation for a prior dependent is deducted, IF the custodial parent in that case files first.
Most states presume that, if/when a summons is served, then that given NCP knows (s)he has a dependent in this world. The presumption is then put forth that any future child(ren) are in addition to, and not instead of, existing child(ren).