WHEN I WAS YOUNG I HAD AN AFFAIR WITH A GIRL WHO WAS NOT A MUSLIM WE BROKE UP AFTER THE CHILD WAS BORN WE NEVER GOT MARRIED AND NOW I DO NOT KNOW WHERE THEIR ABOUTS AND I DO NOT WHERE THE CHILD IS OR IF SHE IS A MUSLIM. WHAT CAN DO TO ASK FOR FORGIVENESS FROM ALLAH FOR MY SIN?
The child is not considered your lawful one and will not be attributed to you (you have no right to paternity) but to the mother. The child is considered like your step-son/daughter and so you are not a mahram (a non-marriageable kin). If the child is a daughter, it is not permissible for you to interact with her, but interaction with a son is permitted. The child does not inherit from you and vice-versa. However you may, if you find him/her, bequeath 1/3 of your wealth to the child but not as inheritance but only as a gift as the child is still your flesh and blood. So you can still take care of your step-child should you locate him/her. But if you could never locate them, then make taubah and never do it again.