She died and left behind a full-brother, a half-brother through her father and her siblings’ children
Question

                A woman died and left behind a full-brother and a half-brother through her father. She also had two other brothers who died during her lifetime, one of whom was a full-brother and the other was a half-brother through her father, and they had children. How should the inheritance be divided?.
Praise be to Allah.
    Firstly: 

    If there is a full brother or a half brother through the 
    father, then the siblings’ children do not inherit. 

    Based on this, then the children of the brothers, in this 
    case, do not inherit anything. 

    Secondly: 
If there is a full 
    brother, then the half-siblings through the father do not inherit anything, 
    whether they are male or female. There is scholarly consensus on all these 
    points. 

    See al-Mughni, 9/22, 23 

    Based on this, the estate in this case should be divided 
    among the full-brother and the full-sister, with the male getting twice the 
    share of the female. The evidence for that is the verse in which Allaah says 
    (interpretation of the meaning): 
“They ask you for a 
    legal verdict. Say: Allaah directs (thus) about Al‑Kalaalah (those who leave 
    neither descendants nor ascendants as heirs). If it is a man that dies 
    leaving a sister, but no child, she shall have half the inheritance. If 
    (such a deceased was) a woman, who left no child, her brother takes her 
    inheritance. If there are two sisters, they shall have two-thirds of the 
    inheritance; if there are brothers and sisters, the male will have twice the 
    share of the female. (Thus) does Allaah make clear to you (His Law) lest you 
    go astray. And Allaah is the All-Knower of everything”

    [al-Nisa’ 4:176]

    And Allaah knows best.