Karna joined the Kauravas and became the friend of Duryodhana. Its true origin was revealed after the war.
In the Mahabharata neither women nor sons are mentioned.
Vrishali, Supriya, and probably others with their sons appear in retellings.
Vrishali – daughter of Satyasena, the charioteer of Duryodhana.
Supriya – friend of Bhanumati, Duryodhana’s wife.
Read about Karna here
Read about Karna’s names here