What is the ruling of Islamic law on claiming custody of a child of unknown parentage as one's own to prevent him from being harmed by society, knowing that he is officially registered as having unknown parents?

It is forbidden to attribute a child whose parents are unknown to oneself. This includes official documents and conversations among people, based on Allah's saying: "Call them by [the names of] their fathers." However, there is no harm in calling a child "my son" or "my dear son" if the intention is to show closeness and endearment, provided there is no confusion.