"Three men were brought to 'Ali while he was in Yemen; they all had intercourse with a woman during a single menstrual cycle. He asked two of them: 'Do you affirm that this child belongs to (the third man)?' And they said: 'No.' He asked another two of them: 'Do you affirm that this child belongs to (the third man)?' And they said: 'No.' So he cast lots between them, and attributed the child to the one whom the lot fell, and obliged him to pay two-thirds of the Diyah. The Prophet was told of this, and he laughed so much that his back teeth became visible."  

أُتِيَ عَلِيٌّ ؓ بِثَلاَثَةٍ وَهُوَ بِالْيَمَنِ وَقَعُوا عَلَى امْرَأَةٍ فِي طُهْرٍ وَاحِدٍ فَسَأَلَ اثْنَيْنِ أَتُقِرَّانِ لِهَذَا بِالْوَلَدِ قَالاَ لاَ ثُمَّ سَأَلَ اثْنَيْنِ أَتُقِرَّانِ لِهَذَا بِالْوَلَدِ قَالاَ لاَ فَأَقْرَعَ بَيْنَهُمْ فَأَلْحَقَ الْوَلَدَ بِالَّذِي صَارَتْ عَلَيْهِ الْقُرْعَةُ وَجَعَلَ عَلَيْهِ ثُلُثَىِ الدِّيَةِ فَذُكِرَ ذَلِكَ لِلنَّبِيِّ ﷺ فَضَحِكَ حَتَّى بَدَتْ نَوَاجِذُهُ  

"While we were with the Messenger of Allah, a man came to him from Yemen and started telling him (about an incident) while 'Ali was still in Yemen. He said: 'O Messenger of Allah, three men were brought to 'Ali who were disputing about a child, and they all had intercourse with a woman during a single menstrual cycle.'" And he quoted the same Hadith.  

بَيْنَا نَحْنُ عِنْدَ رَسُولِ اللَّهِ ﷺ إِذْ جَاءَهُ رَجُلٌ مِنَ الْيَمَنِ فَجَعَلَ يُخْبِرُهُ وَيُحَدِّثُهُ وَعَلِيٌّ بِهَا فَقَالَ يَا رَسُولَ اللَّهِ أَتَى عَلِيًّا ثَلاَثَةُ نَفَرٍ يَخْتَصِمُونَ فِي وَلَدٍ وَقَعُوا عَلَى امْرَأَةٍ فِي طُهْرٍ وَسَاقَ الْحَدِيثَ  

"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."  

كُنْتُ عِنْدَ النَّبِيِّ ﷺ وَعَلِيٌّ ؓ يَوْمَئِذٍ بِالْيَمَنِ فَأَتَاهُ رَجُلٌ فَقَالَ شَهِدْتُ عَلِيًّا أُتِيَ فِي ثَلاَثَةِ نَفَرٍ ادَّعَوْا وَلَدَ امْرَأَةٍ فَقَالَ عَلِيٌّ لأَحَدِهِمْ تَدَعُهُ لِهَذَا فَأَبَى وَقَالَ لِهَذَا تَدَعُهُ لِهَذَا فَأَبَى وَقَالَ لِهَذَا تَدَعُهُ لِهَذَا فَأَبَى قَالَ عَلِيٌّ ؓ أَنْتُمْ شُرَكَاءُ مُتَشَاكِسُونَ وَسَأُقْرِعُ بَيْنَكُمْ فَأَيُّكُمْ أَصَابَتْهُ الْقُرْعَةُ فَهُوَ لَهُ وَعَلَيْهِ ثُلُثَا الدِّيَةِ فَضَحِكَ رَسُولُ اللَّهِ ﷺ حَتَّى بَدَتْ نَوَاجِذُهُ  

"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.  

بَعَثَ رَسُولُ اللَّهِ ﷺ عَلِيًّا عَلَى الْيَمَنِ فَأُتِيَ بِغُلاَمٍ تَنَازَعَ فِيهِ ثَلاَثَةٌ وَسَاقَ الْحَدِيثَ خَالَفَهُمْ سَلَمَةُ بْنُ كُهَيْلٍ  

"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.  

أَبُو عَبْدِ الرَّحْمَنِ هَذَا صَوَابٌ وَاللَّهُ سُبْحَانَهُ وَتَعَالَى أَعْلَمُ