All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Thus, the deceased’s half-sister from the father's side is entitled to half the estate as a fixed share. Allaah, The Exalted, says (what means): {… If a man dies, leaving no child but [only] a sister, she will have half of what he left…}[Quran 4:176]
The residue of the estate is also given to her according to the principle of Radd, given that she is the only eligible heir entitled to inherit.
The same ruling applies if the half-sister is from the mother's side; however, in this case, she gets one-sixth of the estate as a fixed share as well as the residue of the estate under the principle of Radd.
Finally, we would like to warn the questioner that the division of inheritance is a serious and critical matter. It is not adequate to settle for seeking an online Fatwa. Instead, you should refer the case to an Islamic court for investigation; perhaps other eligible heirs would be discovered in the process. Moreover, perhaps the deceased has left a will or was liable to debts or any other obligations of which the heirs are not aware. It is well-known that the repayment of debts and the liabilities are given priority over the heirs’ right to the estate. Therefore, you should not distribute the estate without referring the case to a Sharee‘ah court, if any, in order to preserve the interests of the living and the dead alike.
Allaah Knows best.