The Messenger of Allah ﷺ said, "The child belongs to the bed."
حدثنا سفيان عن ابن أبي يزيد عن أبيه
أن رسول الله ﷺ قال الولد للفراش
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This is a problematic chain of transmission. I fear it may be an error introduced by copyists, for although Yazid bin Abu Ziyad is indeed narrated from by Sufyan bin Uyayna, they did not mention that he narrated from his father Abu Ziyad, nor did they mention this Abu Ziyad among the narrators at all.The hadith was narrated by Ibn Majah (1/316) from Ibn Abu Shayba and Sufyan bin Uyayna, from Ubaydullah bin Abu Yazid, from his father, from Umar, that the Messenger of Allah ﷺ ruled that the child belongs to the marriage bed. Bayhaqi also narrated it in Sunan al-Kubra (7/402) through the route of Shafii, from Ibn Uyayna, with his chain, and it includes a narrative. This chain is sahih. Abu Yazid Makki, the father of Ubaydullah, was mentioned by Ibn Hibban among the trustworthy narrators.So it is very likely that this chain is the original one here, and that the copyists then made an error.