Yes, a common contemporary fraud, and often seen on spurious 1916-D Dimes. A con artist would have a tool akin to a pair of needle nose pliers, with a mint mark punch affixed to one of the jaws. One would then take a genuine 1916-P Dime, and a small hole would be drilled into the rim close to where the mint mark would be located. The jaw with the punch was then inserted into the hole, and the shyster would simply "squeeze" a mint mark out of the metal. Fortunately they are pretty apparent to the discerning eye under 10x magnification and up. Concerning the coin in the OP, I have my bet on it being a forgery. As someone already mentioned the '3' in the date looks extremely suspicious.
The 3s look very similar. Some people collect fakes and such "abnormalities". I have some Henning nickels, known counterfeits. I also have some large silver coins that are commonly faked. Coins that I need to get x-rayed. Coins such as the Austrian Theresa Thalers, the French Indo-Chine Piastre trade dollars, Morgans, etc.. Maybe the book the coin was found in just happened to have a fake coin because the previous owner knew it was fake and was just keeping it for "fun". Who really knows?
I would keep it also as for interest. Unfortunately for me the dealer had to have it back to get his retainer back
Many of the people who gave you answers are extremely knowledgably. You can try elsewhere or spend (waste) money sending it a TPG, but you would be wasting your time
Remember there are very few of these. And the ones that are known, are all listed, documented, etc. While a new discovery is possible, there are millions of fakes and altered coins and pretty much anytime anyone thinks they have one of these, it's not going to be genuine. But when it's in your possession, you want to believe.