I told them I was always late because of a medical reason
Is that so? Is this the first time you explained that reason to them?
No, I have told them multiple times.
There is nothing wrong with having a disability.   It is wrong to fake having one or use it as an excuse when it is not a hindrance.   You could permanently lose credibility if they ever found out.
They think I'm a genius for working hard. I'm going to take it for myself.
It's great they see you as a valuable employee, but don't you think it's a little too much taking advantage of their opinion on you with a fake disability? How about owning up to your image and being honest, so they have more reason to look up to you.