What is the story of the incident involving the man accused of having an affair with the Prophet's ﷺ concubine, and how did the Prophet order his execution for the charge of adultery, even though it was discovered that he was impotent?

This hadith is in Sahih Muslim and was mentioned by Ibn al-Qayyim in "Zad al-Ma'ad." Its summary is that the Prophet, peace and blessings be upon him, ordered Ali ibn Abi Talib to kill a man accused of adultery with Mariya. When Ali found him, it became clear that he was majbub (had his penis cut off), so Ali refrained from killing him.

Scholars differed in interpreting this command: 1. Some challenged the authenticity of the hadith. 2. Some interpreted the command to kill as not intending actual killing, but rather to frighten him into deterrence, or to reveal the truth of his condition, similar to what Solomon, peace be upon him, did in the story of the two women and the child. 3. The better interpretation is to say that the Prophet, peace and blessings be upon him, commanded his killing as a disciplinary measure (ta'zir) for daring to be alone with the mother of his child. When Ali became certain of his innocence from suspicion, he refrained from killing him. 4. Al-Nawawi said: Perhaps he was a hypocrite and deserved to be killed for another reason besides adultery, and Ali refrained from killing him because he knew that adultery had not occurred.