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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is not permissible for a man to marry a woman with whom he had illegal sexual intercourse according to the preponderant opinion of Muslim scholars. If she sincerely repents and she completes her waiting period (to ascertain not being pregnant) then he may marry her. The waiting period of a pregnant woman is until she gives birth.
However, as long as the marriage has been conducted then there is no harm to continue it, according to those scholars who believe that the marriage of the woman who becomes pregnant by illegal sex is valid.
The illegitimate child is not traced back to you according to the majority of Muslim scholars, rather he is traced back to his mother. He also inherits from his mother (and not you) and the mother inherits from him.
It is mandatory on every Muslim to avoid having illicit relations and you both must repent from this sin.
Allaah Knows best.