It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) said: "Give the fixed shares (fara'id) to those entitled to them, and whatever remains after the fixed shares goes to the nearest male relative."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12376
Hakim bin Iqal (may Allah have mercy on him) said: The case of a woman was brought to Shurayh (may Allah have mercy on him); she had left behind two sons of her paternal uncle, one of whom was her husband and the other her maternal half-brother. Shurayh (may Allah have mercy on him) gave the husband half and gave the rest to the maternal half-brother. This reached Sayyiduna Ali (may Allah be pleased with him), so he sent for Shurayh (may Allah have mercy on him) and said: "Call this insolent slave to me." When Shurayh was called, he said: "What did you rule?" Shurayh (may Allah have mercy on him) said: "I gave the husband half and gave the maternal half-brother the remainder." Sayyiduna Ali (may Allah be pleased with him) said: "Did you rule this by the Book of Allah or by a Sunnah of the Messenger of Allah (peace and blessings be upon him)?" Shurayh (may Allah have mercy on him) said: "By the Book of Allah." Sayyiduna Ali (may Allah be pleased with him) asked: "Where?" Shurayh (may Allah have mercy on him) recited: "And those of blood relationship are more entitled to one another in the Book of Allah" [Surah al-Anfal: 75]. Sayyiduna Ali (may Allah be pleased with him) said: "Does it say: half for the husband, and the rest for this one?" Then Sayyiduna Ali (may Allah be pleased with him) gave the husband half and gave the maternal half-brother a sixth. Then he divided the remainder between the two of them.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12377
It is narrated from Sayyiduna Ali (may Allah be pleased with him) that two sons of a paternal uncle were brought to him, one of whom was a maternal half-brother. Sayyiduna Ali (may Allah be pleased with him) was told: Abdullah (may Allah be pleased with him) used to give the whole property to the maternal half-brother. Sayyiduna Ali (may Allah be pleased with him) said: "May Allah have mercy on him; although he was a jurist, had it been me, I would have given the maternal half-brother a sixth, then divided the rest between the two of them."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12378
It is narrated from al-Sha'bi concerning a woman who leaves behind two sons of her paternal uncle, one of them her husband and the other her (maternal half-)brother: according to the view of Ali and Zayd (may Allah be pleased with them both), the husband gets half and the maternal half-brother a sixth, and the two of them share in the remainder; and according to the view of Abdullah (may Allah be pleased with him), the husband gets half and all the rest goes to the maternal half-brother.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12379