What is the ruling of Islamic law regarding a man who discovered his wife's infidelity, her pregnancy and her giving birth to a son from her lover, and he confirmed that the son is not his; should he divorce her, or live with her, or what should he do?

Adultery (zina) is a major sin and a grave abomination. It is even more sinful and reprehensible when committed by a married woman. The general principle is to assume the best of a Muslim and to verify before accusing a wife of betrayal. If the wife's adultery is proven by her confession and she repents, it is better to keep her and treat her kindly. However, if she persists in her wrongdoing, then it is preferable to separate from her. If the wife becomes pregnant, the child is attributed to the husband, who is the owner of the bed, unless he denies paternity through li'an (oath of condemnation). The husband must protect his wife by preventing her from mixing with non-mahram (definition) men and guiding her towards good, and by being a good role model for her.