Husbands rights

My wife has a son by another man. She had an affair approx 2 years ago and the little boy is the result.
His biological father wants nothing to do with him and I am the only father he has ever known.

Do I have any rights whatsoever where this child is concerned?
Do I have to adopt him and if so what if his biological father will not cooperate?
My wife and I have been married for 10 years now and after some rough patches we just want to be a family and raise our son the best way we can.

We currently live in Chicago.

According to a website on paternity in Illinois:
What is "legal paternity"?

Paternity is the relationship between a father and his child. Legal paternity is paternity established by law. State law recognizes only the legal father as having certain rights and responsibilities. In Illinois, a man is a child's legal father only if one of the following is true:

• He was married to the child's mother when the child was born or when the child was conceived (or both)
• He married the mother after the child's birth and he is listed with his permission (as of August 9, 1996, his written permission is needed) on the child's birth certificate as the father
• There is a court order or Department of Public Aid administrative order of paternity
• He and the mother have signed a voluntary "acknowledgement of parentage" or "acknowledgement of paternity" form

If legal paternity has not been established, the man has no right to ask a court for custody or visitation with a child, and the child's mother cannot try to have a court order the father to pay child support.

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Who is listed as the child's father on the birth certificate? Why aren't you listed since you were married to the mother at the time of the child's birth?