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 is His slave and Messenger.
These two children are considered your brothers from your mother’s side as you all have the same mother and they are traced back to her since the child of Zina (fornication or adultery) is traced back to his mother and he inherits her and she inherits him as we clarified in Fataawa 89082 and 85430, so it is important that you refer to them.
Based on the above, these two children have their right upon you as brothers.
On the other hand, we advise you to do your utmost to save your mother from Hellfire by bringing her back to the truth and make her repent from apostasy. First, you should supplicate Allaah for her as supplication is the weapon of the believer by which he achieves his needs. Indeed, Allaah urged us to supplicate Him and He promised us to answer our supplication. Allaah says (what means): {And your Lord says, Call upon Me; I will respond to you.” Indeed, those who disdain My worship will enter Hell [rendered] contemptible.}[Quran 40:60]
Then, you should seek the help of righteous and pious people and scholars so that they would clarify to her the seriousness of apostasy which leads to the wrath of Allaah and losing this world and the Hereafter, and this is the manifest loss. Allaah says (what means): {And whoever of you reverts from his religion [to disbelief] and dies while he is a disbeliever -for those, their deeds have become worthless in this world and the Hereafter, and those are the companions of the Fire; they will abide therein eternally.}[Quran 2:217]
For more benefit, please refer to Fatwa 87672.
Allaah knows best.