It looks like you have half of a Magicians coin. I'm not sure if to many magicians coins were created out of cents. I would think the milling of the cents would not be a easy task compared to the larger coins. Wait for a expert to chime in with their opinion.
The Lip is the same all away around the edge. It looks like your second photo you have listed of the Jefferson nickle. Can you tell me how this happens? I think it's kinda neat, my first "oddity" coin.
But there is another cause of an area that leaves the rim rough and uneven. That is the removal of a coin in a "Good Luck" holder. When the coin is removed it reveal how it was pressed into the hold and now the coin is ruined. So best to leave these in the holder. At least they are sell able in tact.
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