What should a person do who committed adultery with a married woman, and she became pregnant by him and gave birth to a child, and then the woman was divorced after a period of time; should he marry her and raise his son, or what?

You must repent from adultery. The child belongs to the marriage bed, based on the Prophet's (peace be upon him) saying: "The child is for the bed, and for the adulterer is the stone." This means that the child is attributed to the woman's husband if she is married. Scholars differed regarding the condition of the possibility of intercourse after the marriage contract; the majority stipulate it, except for Abu Hanifa. This child is not yours. Your marriage to the adulterous woman is permissible if she repents; otherwise, it is a matter of scholarly disagreement.