Is the marriage valid, and what is the ruling concerning the child in this case according to Islamic law?

The questioner must repent to Allah for the abomination of adultery. If he marries the woman with whom he committed adultery, with the consent of a guardian and witnesses, the child born of adultery is not attributed to him according to the majority of scholars. However, some scholars hold the view that it is permissible to attribute the child to him if the marriage is valid. If the aforementioned marriage took place without a guardian and two witnesses, it is not considered valid, and separation is immediately required. If they wish to marry, a contract must be drawn up that fulfills the conditions, such as a guardian and witnesses. If the woman does not have a Muslim guardian, then her guardian is the judge. As for her embracing Islam, it is achieved by uttering the two testimonies of faith, not through a mufti (definition) or a court. Then, she must fulfill the religious obligations and avoid prohibitions.