What is the ruling on those who converted to Islam and had a previous relationship with the other sex and she or he (i.e the one who converted to Islam) had illegitimate children out of this relationship?
What is the ruling on those children? How should their Muslim parent deal with them Islamically?
Please, enlighten me in this regard in details.
May Allah reward all of you.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Any child that results from Zina (a relation outside wedlock) regardless of whether his parents are Muslims or one of them is Kafir (non-Muslim), this child is traced back to his mother and they [child and mother] inherit each other.

The fornicator has no relation to them and they are, by no means, traced back to him. So, this father deals with them in the same way he deals with any non-Mahram person except as far as marriage is concerned, because it is forbidden for the man to marry his daughter from Zina, according to the majority of scholars.

Allah knows best.