I remember reading this at school when I was 12 or 13, so I assume this is a sci-fi story for kids. I also remember that the story is a bit old too.
The story, from what I remember, is about a boy who goes into a doctor's/scientist's lab and finds out he created a cloning machine. I can't really remember if the doctor cloned himself, but I believe he did, and that both the clone and the original killed each other (or something like this).
After that, the boy clones himself and hides this clone from his family. At first, things go well, until both of them get into a fight in the lab, which ends up with one of the boys dying. The plot-twist is that the narrator is the clone and we find that out in the end, when the clone sees that a mole on his face is on the other side. Basically, the clone did not know he was the clone, because he had the memories of the original boy. The reason the mole is on the other side is because clones are a mirrored version of the original.