When I was young, I had a lot of sexual encounters and never thought too much about my promiscuity. However, I am now older and have obeyed the Gospel, but I wonder from time to time whether I might have fathered a child. No one has ever come forward concerning this matter, but I can't keep from wondering and worrying about it. If there is someone I am the father of and I don't know about it, can I be forgiven by God, or am I doomed to hell because of this horrible sin I might have committed?
Becoming a Christian requires, among other things repentance and baptism. "Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit"" (Acts 2:38). Repentance is changing your mind about sin and changing your behavior (II Corinthians 7:10-11). That is something have done regarding your sexual sins. The goal is that someone meeting you today or in the future would never guess that you used to be promiscuous.
In repenting, we cannot undo the past, but we can take responsibility for what we did and try to minimize the damage as best we can, knowing that some things just cannot be corrected. You have no idea if you fathered any children, but you can resolve that if become aware of a child who is yours, that you won't avoid taking responsibility. It means that before you get married, you need to tell your future wife that you had a bad past and you have no idea if that past will come back to haunt you. This way she won't feel like she was caught off guard if it does come up. That is the best you can do for right now.
The sin wasn't in possibly fathering children outside of marriage. The sins were in the lust, lewd behavior, and fornication that you were doing. If a pregnancy had occurred, it was just a side-effect of the fact that you were sinning.
When you were baptized all your past sins were done away with (Romans 6:3-7). You started a new life that doesn't revolve around sin.