Where was a penny stamped with a p made?

Because no US cents carry a P mint mark, it's pretty certain that you have a mint medallion from the Philadelphia Mint. They're struck on the same blanks used for cents, but have either a large P for the Philadelphia Mint or D for Denver.

Mint medallions are included with uncirculated coin sets sold by the US Mint to collectors. However, the medallions themselves aren't really collectible. They don't have years on them so there's no way to tell one year from another.