I can answer only in terms of Indiana law, so with that in mind:
The court can ORDER a paternity test. If he does not comply by the deadline, the court can find him in contempt and can jail him, fine him or impose community service.
If a lot of those loser fathers could get out of their responsibilities so easily, they'd ALL be doing it.
There are mechanisms in place to ensure that he supports his child -- but first the court will want to establish paternity.
The courts have seen/heard it all -- and know how to deal with Mr. Reluctant.