My mother never knew who her biological mother was. Her real father,whom she grew up with, was named John Hamilton Dunlop. He was born in Glascow Scotland in the late 1800s. He had a brother named George. He was married to Elizabeth Gibb Dunlop. Any info would be greatly appreciated as she was never able to find any info.

It is not likely that there IS a record from that time.

Honestly, researching it after all this time is going to be VERY difficult, because it is likely the biological mother was kept VERY secret so that her reputation was not ruined. It may not have ever been filed in courts at all, especially since the child grew up with the biological father.

I assume that he knew who she was and just never said, since he was the biological father? I would also assume that it was an affair that he had that resulted in her conception?

You can try to find someone who was a child at the time and remembers the scandle, but it's unlikely you will. You could also hire a private detective to search for you, but again, it is unlikely that after this long you will find much information.