He died and left behind a wife, a full sister and half-brothers and –sisters through his father

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.