There is no musaah in Islam

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) said: "There is no room in Islam for musa'ah (claiming lineage through fornication with a slave woman). Whoever made such an attempt in the Days of Ignorance, I have attached him to his 'asabah. And whoever claims a child (as his own) born without marriage (as a result of fornication), that child will neither inherit (from the claimant) nor be inherited from."
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.

Amr bin Shu'ayb narrates from his father, from his grandfather, that the Prophet (peace and blessings be upon him) said: "Whoever claims a child born of a slave woman whom he did not own, or (claims a child) of a free woman with whom he committed fornication, that child will not be attached to him (the claimant) nor will he inherit from him. He is a child of fornication and will be counted among his mother's family, whoever they may be."

It is narrated from Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "Full siblings (sharing both mother and father) inherit from one another, to the exclusion of half-brothers (sharing only the father)."

It is narrated from Sayyiduna Jabir bin Abdullah (may Allah be pleased with him) that the wife of Sayyiduna Sa'd bin al-Rabi' (may Allah be pleased with him) came (to the Prophet, peace and blessings be upon him) and said: "O Messenger of Allah! These are the two daughters of Sa'd bin al-Rabi'. Their father was martyred with you at the Battle of Uhud, and now their paternal uncle has taken all their wealth and has left nothing for them." He (peace and blessings be upon him) said: "Allah Almighty will decide concerning this." The narrator said: Then the verse of inheritance was revealed, and the Messenger of Allah (peace and blessings be upon him) sent for their uncle and said: "Give the two daughters of Sa'd two-thirds, give their mother one-eighth, and whatever remains is yours."
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.