Illegitimate Child, Can Be Ascribed to His Father?
Answering your question, Dr. Main K. Al-Qudah, a member of the Assembly of Muslim Jurists in America (AMJA) stated,
In addition to the sincere repentance to Almighty Allah because of what you did, you need to keep taking care of the child, not to mention anything to him.
Furthermore, if his mother was single when you both committed such sin together, you can claim the child legally and attribute him to you as your son. The latter is a recent fatwa issued by AMJA.
As you see, it considers the bad consequences of leaving those illegitimate kids alone without appropriate parenting.
May Allah forgive your sin and help bring up this kid upon Islam.