What is the Sharia ruling on establishing the paternity of a child born out of wedlock to his father who acknowledges him, and what are the views of the Islamic schools of thought on this, taking into consideration the principle of preserving the lineage of the child and the problems faced by illegitimate children?

If a man confesses to adultery, he deserves the prescribed Islamic punishment (hadd). The child born from this act is attributed to him if no one disputes it and the adulterer acknowledges the child. This is the view of some scholars. However, the majority of scholars hold that a child born from adultery is not attributed to the adulterer nor is he related to him, based on the hadith: "The child is for the bed [legitimate marriage], and for the adulterer is the stone [punishment]." This view of the majority of scholars is closer to correctness, even though adopting the other opinion might avert a greater harm, in which case there would be no objection to it. As for official documents, the child can be nominally attributed to a father (e.g., "son of Abd al-Rahman") so that he may be a male relative (mahram) to his mother.