Praise be to Allah.

The estate of this deceased person is to be distributed in the following manner: 

With regard to the wife, she is entitled to one quarter, because there are no descendants who inherit. Allah, may He be exalted, says (interpretation of the meaning):

“their (your wives’) share is a fourth if you leave no child; but if you leave a child, they get an eighth of that which you leave after payment of legacies that you may have bequeathed or debts”

[an-Nisa’ 4:12]. 

With regard to the sons of the half-brother through the mother, they come under the heading of dhawi’l-arhaam (distant relatives through the female). The most correct scholarly view is that the dhawi’l-arhaam may inherit in the case when there are no heirs with allocated shares or residuary heirs, except a husband or wife. 

Ibn Qudaamah said in al-Mughni (6/317), when discussing the issue of dhawi’l-arhaam:

They are the relatives who do not have an allocated share and are not residuary heirs. There are eleven types: daughters’ sons, sisters’ sons, brothers’ daughters, sons of siblings through the mother, paternal aunts, the paternal uncles of the mother, maternal uncles, maternal aunts, daughters of paternal uncles, maternal grandfathers and the mothers of great-grandfathers. All of these, and those of their descendants who take their place, are called dhawi’l-arhaam. Abu ‘Abdullah regarded them as heirs if there were no heirs with allocated shares, no residuary heirs, and no heirs except the husband or wife. End quote. 

This has been discussed previously in detail, in fatwas no. 85495 and 176434. 

Moreover, the view expressed in the fatwa regarding the way in which dhawi’l-arhaam relatives inherit is the view of the majority of the later Maalikis and Shaafa‘is, and it is the view of the Hanbalis, with regard to what may be called replacement, which means that any one of the dhawi’l-arhaam may take the place of his immediate ascendant or relative who would have been an heir and receive the share that he would have received. 

For example: the daughter’s son inherits the share of the daughter, the maternal uncle inherits the share of the mother, the daughter of a full brother inherits the share of the full brother, and the son of a half-brother through the mother inherits the share of the half-brother through the mother. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said, when discussing the inheritance of dhawi’l-arhaam relatives: 

There are some scholars who say that they inherit by virtue of replacement, i.e., the one who is present takes the place of his immediate ascendant or relative. This is the view followed by the author (may Allah have mercy on him), who said: “They inherit by virtue of replacement”, meaning that each one takes the place of his immediate ascendant or relative. So the mother’s father takes the place of the mother, and is entitled to the mother’s share of inheritance. The sister’s son takes the place of the sister, and is entitled to the sister’s share of inheritance. The son of a half-brother through the mother takes the place of the half-brother through the mother, and is entitled to the half-brother’s share of inheritance. Thus they inherit by virtue of replacement.

End quote from ash-Sharh al-Mumti‘ ‘ala Zaad al-Mustaqni‘ (11/274) 

Based on that, in this case the sons of the half-brother through the mother inherit one sixth of the estate of the deceased, then they may inherit whatever is left of the estate after it has been divided. 

With regard to the one sixth, that is because it is the share of their father – who is the half-brother through the mother – which is his allocated share in the event that he is the only heir, because Allah, may He be exalted, says (interpretation of the meaning):

“If the man or woman whose inheritance is in question has left neither ascendants nor descendants, but has left a brother or a sister, each one of the two gets a sixth; but if more than two, they share in a third”

[an-Nisa’ 4:12]. 

Ibn Qudaamah (may Allah have mercy on him) said: What is referred to in this verse is the half-brother or -sister through the mother, according to scholarly consensus. The phrase translated here as “…has left neither ascendants nor descendants”, according to the majority, refers to one who leaves behind neither a child nor a parent. So in order for the siblings to inherit, it is stipulated that there should be no child or parent; the word translated here as child includes both males and females, and the word translated as parent includes both the father and grandfather.

End quote from al-Mughni (6/163) 

The children of the half-brother through the mother inherit the share of their father, which is one sixth; it is to be shared equally among them, with each female getting the same share as each male – if there are females among them. 

It says in ash-Sharh al-Mumti‘ ‘ala Zaad al-Mustaqni‘ (11/275), in a discussion on the inheritance of dhawi’l-arhaam: If they inherit by taking the place of those whose shares are the same for both males and females, then their males and females inherit equal shares; if they inherit by taking the place of those whose shares are different for males and females, then their shares differ. The shares of children of siblings through the mother are equal, so if a person dies and leaves behind a daughter of a half-brother through the mother and a son of a half-brother through the mother, then they inherit equal shares, because they took the place of those whose shares are the same for both males and females. End quote. 

With regard to the remainder of the estate, the sons of the half-brother through the mother may take it, and it is to be divided among them equally. The wife does not take any share of it, because spouses have no share of the remainder. 

It says in al-Mughni by Ibn Qudaamah (6/296): With regard to spouses, they have no share of the remainder of the estate according to scholarly consensus.

End quote. 

In fatwa no. 166553, we explained that with regard siblings through the mother, whether they inherit through allocated shares or they inherit what remains after allocated shares have been calculated, their inheritance is to be divided among them equally, with the share of each female being like the share of each male. It is to be shared out in like manner among their children, with the share of each female being like the share of each male. 

Finally, we should point out that the estate of the deceased is to be inherited according to the limits of sharee‘ah that are set out by Allah, may He be glorified, in His Book, whether the estate was acquired by means of inheritance or by means of hard work, engaging in business or manufacturing, and so on, or as a gift or by some other permissible means. None of that has any effect on the division of inheritance. 

And Allah knows best.