I have this unusual looking penny...It is not only magnetic but also over sized with a lipped rim and the back has a distinctive copper silver rim that appears almost like its been capped
It has some sort of bezel on it, probably from jewelry or a key ring. The bezel is the magnetic part, just a normal Lincoln cent.
I know the photo looks like there is an added rim, but this is in one solid piece the end is bent ,,,I used a high magnifing jeweler glass to get the photo
It's a rolled bezel that's been brazed to the coin on the obverse to give a seamless appearance. That would be my guess.
Your second photo clearly shows the bezel. You can choose to accept the reality that you have an ordinary coin in a bezel or you can ignore the opinion of experienced collectors and continue to believe you have some sort of rare and valuable error. If you choose the second option it won't be the first time we have witnessed that.