Grading: Its chain is da'if (weak).
Technical note / Defect ('illah): Because the narrator who reports it from the Prophet (peace and blessings be upon him) is "mubham" (unnamed). In some narrations he will be attributed to "Banu Zurayq", and it will also appear that he asked people about this matter and did not hear it from the Prophet (peace and blessings be upon him) himself; so, besides being unnamed, it is also "mursal". And Allah knows best. Al-Bayhaqi counted it as munqati' in his "Sunan".

Technical note / Defect ('illah): There is disagreement about who 'Abdullah bin 'Ubayd, from whom Dawud bin Abi Hind narrates, is. Al-Bukhari and Ibn Abi Hatim counted him as "al-Ansari", and this one is majhul (unknown); whereas al-Thawri and Hammad named him "'Abdullah bin 'Ubayd bin 'Umayr". In al-Thawri's narration with al-Bayhaqi he is attributed to the Ansar, while in the narration of Ibn Jurayj it says: "'Abdullah, meaning Ibn 'Ubayd bin 'Umayr". Al-Khatib in "Mudih al-Awham" considered it preponderant that this 'Abdullah bin 'Ubayd is in fact "Ibn 'Umayr al-Laythi", and he is a "trustworthy and well-known" narrator.

Reference / Source: Abu Tahir al-Mukhallis narrated it in "al-Mukhallisiyyat" (2836) from 'Abdullah bin Muhammad al-Baghawi, from 'Abd al-A'la bin Hammad, with this same chain.

Reference / Source: Abu Dawud narrated it in "al-Marasil" (362) - and via him al-Bayhaqi (6/ 259) - from Musa bin Isma'il, from Hammad bin Salamah, likewise. Its wording is: "The 'asabah of the child of the woman who underwent li'an are the 'asabah of his mother." Al-Bayhaqi said: It is munqati'.

Reference / Source: 'Abd al-Razzaq (12477), Ibn Abi Shaybah (10/ 170, 11/ 339), al-Darimi (3002), al-Bayhaqi (6/ 259) and al-Khatib in "Mudih al-Awham" (1/ 136-137) narrated via Sufyan al-Thawri, from Dawud bin Abi Hind, from 'Abdullah bin 'Ubayd bin 'Umayr, who said: "I wrote to a brother of mine among Banu Zurayq: In whose favour did the Messenger of Allah (peace and blessings be upon him) rule concerning the child of the woman who underwent li'an? He wrote back to me that the Messenger of Allah (peace and blessings be upon him) ruled in favour of his mother; she stands in the place of both his father and his mother."

Reference / Source: 'Abd al-Razzaq (12476) narrated it from Ibn Jurayj, from Dawud, from 'Abdullah (meaning Ibn 'Ubayd bin 'Umayr), who said: "I wrote to a man of Banu Zurayq from the people of Madinah asking who inherits from the child of the woman who underwent li'an. He wrote back to me that he had asked (people), and they agreed that the Prophet (peace and blessings be upon him) ruled in favour of the mother, and placed her in the position of both his father and his mother."
Technical note / Defect ('illah): This narration indicates that the unnamed man from Banu Zurayq who gave the report did not hear it himself from the Prophet (peace and blessings be upon him), but rather asked the people of Madinah about it.

Corroborating chains and supporting reports: In the hadith of 'Amr bin Shu'ayb, from his father, from his grandfather, it is mentioned that the man in the li'an story was a "Zuraqi" (of Banu Zurayq), as narrated by al-Nasa'i (6328) and others.