I have seen a few of these over the years. Definitely Post Mint alteration. Someone skillfully cuts out a small round circular section of a Wheat Cent then attaches it facing the other way around. It is intersesting but just damaged.
It looks like some sort of hollow, circular cutting tool was used to cut out the center and reverse it in the coin. ~ Chris
Definitely a punch and plug, as @Robert Ransom already mentioned. I must say it was done with skill to fit so perfectly, but still just a damaged cent. Nice novelty to have for show and tell. Can't quite make out the date, but thank you so much for posting Full Image photos of obverse and reverse and welcome to CT.