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

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.