Praise be to Allah.
If the heirs of the deceased are as mentioned in the question, the estate is to be divided as follows:
The wife gets one-quarter, because Allaah says (interpretation of the meaning):
“In that which you leave, their (your wives) share is a fourth if you leave no child”
[al-Nisa’ 4:12]
The full sister gets half, because Allaah says (interpretation of the meaning):
“If it is a man that dies leaving a sister, but no child, she shall have half the inheritance”
[al-Nisa’ 4:176]
The rest, which is one-quarter, goes to the half-siblings through the father, males and females, to be shared among them with each male getting twice the share of a female, because Allaah says (interpretation of the meaning):
“if there are brothers and sisters, the male will have twice the share of the female”
[al-Nisa’ 4:176]
And Allaah knows best.
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