What is the ruling on an adult addressing a young boy or girl as "my son" or "my daughter" when he is not their father, if this practice is customary in society, and is this considered an impugnment of the mother's honor?

It has become customary for people to address those who are not their children with "ya bunayya" (O my son) or "ya ibni" (O my son) out of leniency and a desire for closeness. This is a broad matter and there is no harm in it. The intention behind it is kindness and closeness, and it has no connection to proving or disproving lineage. This meaning is evident in the religious texts. The monk said to the boy in the story of the People of the Ditch: "O my son, you are better than me today." And A'idh ibn Amr said to Ubayd Allah ibn Ziyad: "O my son, I heard the Messenger of Allah, peace be upon him, say: 'The worst of shepherds is the one who is harsh.'" And Asma' said to her freed slave: "O my son, has the moon set?" Imam Muslim titled a chapter in his Sahih (definition): "Chapter: The permissibility of saying 'O my son' to someone who is not one's son, and its desirability for tenderness." And Anas narrated that the Prophet, peace be upon him, said to him: "O my son." And Al-Nawawi stated that this is desirable if the intention is kindness. Al-Bukhari titled a chapter in "Al-Adab Al-Mufrad": "Chapter: A man saying 'O my son' to a young person," indicating that this address is made out of mercy.