If a man finds out that the child he has been supporting, spending money, on, and sheltering is not his, will the woman ever be made to reimburse him the money he has spent sheltering and supporting that child while he was deceived into thinking it was his child by the woman?

Maybe.

Were they married when the child was born?

What evidence does he have that she deceived him, as opposed to simply being unsure as to who the father was.

What jurisdiction (U.S. state or foreign country) are they in?