"The Messenger of Allah sent 'Ali to (be the governor of) Yemen, and a child was brought to him concerning whom three men were disputing." Then he quoted the same Hadith. Salamah bin Kuhail contradicted them.
Sunan an-Nasa'i Book 27, Hadith 103
← Previous Hadith "I was with the Messenger of Allah, and 'Ali, may Allah be pleased with him, was in Yemen at that time. A man came to him and said: 'I saw 'Ali when three men were brought to him who all claimed (to be the father) of a child. 'Ali said to one of them: Will you give the child up to him? And he refused. He said to (the next one): Will you give the child up to him? And he refused. He said to (the next one): Will you give the child up to him? And he refused. 'Ali said: You are disputing partners. I will cast lots among you, and whoever wins the draw, the child is for him, and he has to pay two-thirds of the Diyah.' The Messenger of Allah laughed so much that his back teeth became visible."

Sunan an-Nasa'i Book 27, Hadith 102 Next Hadith → "I heard Ash-Sha'bi narrating from Abu Al-Khalil or Ibn Abi Al-Khalil that three men had intercourse (with the same woman) during a single menstrual cycle;" and he mentioned something similar, but he did not mention Zaid bin Arqam or attribute anything to the Prophet.

Sunan an-Nasa'i Book 27, Hadith 104