What is the ruling of Islamic law regarding someone who gives his name to a person who is not his biological child, or to a child born out of wedlock before marriage? And do civil laws apply in these cases? And what is the ruling on establishing paternity through DNA tests?

Adoption is forbidden in Islam. It is the act of a man attaching to himself a child of unknown or known lineage. Jurists have differed on the permissibility of a father claiming paternity of his child born out of wedlock. The majority view is that it is not permissible, while Abu Hanifa allowed it if the father married the woman with whom he committed adultery.

Lineage in Islam is established by the matrimonial bed (marriage contract), and DNA testing is not considered for proving paternity when a marriage contract exists. Rather, it is resorted to for verifying paternity before mula'anah (oath of condemnation) with specific conditions. As for a child born out of wedlock, he is not legally attributed to the adulterer, even if medical testing proves his lineage to him.