Inheritance of paternal half-brothers

It is narrated from Sayyiduna Ali (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) ruled that debt is to be paid before the bequest, even though you recite it (in the Qur'an) as: "after any bequest he has made or debt" [Surah al-Nisa: 11]; and that full brothers (children of the same mother and father) inherit from one another to the exclusion of paternal half-brothers (sharing only the father); and that full brothers (sharing both mother and father) are nearer than brothers sharing only the father.
People have narrated this hadith by way of Abu Ishaq and al-Harith, and for that reason the two Shaykhs did not record it; however, this same fatwa is also authentically established from Sayyiduna Zayd bin Thabit.

Kharijah bin Zayd bin Thabit narrates from his father, Sayyiduna Zayd bin Thabit (may Allah be pleased with him), that the ruling on the inheritance of paternal half-brothers (sharing only the father), when there is no full brother (sharing both mother and father) with them, is exactly the same as that of full brothers: their males are like the males (of full brothers) and their females like the females. But when full brothers and paternal half-brothers are together, and there is a male among the full brothers, then the paternal half-brothers have no share in the inheritance.

It is narrated from Sayyiduna Zayd bin Thabit (may Allah be pleased with him) concerning "the shared case (al-mushtarakah)" (in which the husband, the mother, maternal half-brothers and full brothers are the heirs) that he said in favour of the full brothers: "Suppose that their father was a donkey; the father's share (in their lineage) has only increased their closeness (to the deceased)." So he made the full brothers share with the maternal half-brothers in the one-third (1/3).
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Imam al-Sha'bi (may Allah have mercy on him) that Sayyiduna Umar, Sayyiduna Ali and Sayyiduna Zayd (may Allah be pleased with them) gave this ruling concerning a mother, a husband, full brothers and maternal half-brothers: the full brothers will share with the maternal half-brothers in their one-third (1/3), because they said that they are all the children of one mother, and the father's share (in their lineage) has only increased their closeness; therefore they will all share in the one-third.