Does a paternal half-brother inherit from the estate of his father's deceased wife?

Your paternal half-brother does not inherit from your mother, but he inherits from his father all that remained in the father's possession at the time of his death. Regarding the house, if its registration in the mother's name was merely due to her efforts and she did not pay from her own money, then this mere registration does not make it her property. Instead, it remains for the heirs and is distributed among them according to Islamic law. However, if she paid from her own private money when it was purchased or built, then she owns a portion of the house commensurate with what she paid, and the remainder belongs to the husband. If the house was registered in her name as a bequest after his death, then it is a bequest to an heir, which is not valid unless the heirs, including your paternal half-brother, consent to it. If it was a gift and the mother was able to dispose of it during his lifetime, it became her property and does not enter into his estate. However, if she was unable to dispose of it or if it remained with her until he died, then it is an incomplete gift, and the house is an inheritance for the heirs.