Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
The children whose mother is married to a man not their father do not inherit from the husband of their mother. They are neither among those mentioned in Qur'an who have specific shares designated for them, nor are they Asabah (the blood relatives from father's side who inherit after those who have their fixed shares in inheritance), nor are they among blood relatives of their mother's husband.
Allah knows best.