Praise be to Allah.
In the case of those who had intercourse when they were kaafirs, if they believed that this intercourse came under a marriage contact that they regarded as valid – even though it is invalid according to sharee’ah – then the children belong to the man. For example, when he was a kaafir, a man proposed to a woman that she should be his wife and she agreed, and they thought that this was a marriage contract, then the man and woman become Muslim. In this case we say that their marriage contract is valid and does not need to be renewed, and the children that they have had together belong to them, unless the wife is not permissible for the husband when they become Muslims, such as if he was a Magian and married his sister – because the Magians regard marriage to mahrams as permissible. If he married his sister when he was a kaafir then he became Muslim, and she also became Muslim, then they must be separated, because the woman is not permissible for the man. So we say to those who are mentioned: If you believe that your relationship with this woman was marriage, then it is not zina, and the children belong to you. If you believe that it was zina, then if you accepted these children as yours when you were kaafirs, then they are also your children as Muslims, so long as there is no one else claming them as his. If they did not accept them as their own, then they cannot be their children.
With regard to maintenance, if we rule that they are their children, then they are obliged to spend on them, and if we rule otherwise then they do not have to spend on them.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him).
Liqaa’aat al-Baab il-Maftooh (3/385-386).