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 ʻalayhi wa sallam, is His slave and Messenger.
These children do not bear your father's name and he is not considered their father in the Shareeʻah. Accordingly, they are not among your Mahrams and you are not related to them. Please refer to Fataawa 84303 and 89082.
As for your children, you may tell them that these children are not your father's children and are not your siblings without going into details. If one of them happens to ask about the details, you may resort to Tawriyah (equivocation or double entendre, that is, using an ambiguous kind of language to make the listener understand something else) without informing them of the fact that they are illegitimate children or that you father had an illicit relationship with a woman or the like.
Allaah Knows best.