1776 New Hanpshire half penny Very Rare!!

Astute observations, sir. Well done!

 

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Yours is definitely a replica. The New Hampshire coins are kind of an enigma, no one is certain that any originals exist or were even made. The first picture in the book that you posted is generally considered to be the original. The other that matches yours is actually an old fake, yours is a copy of a fake. To add to that you can see where the copper plating is chipping off of yours revealing the base metal of a cheap souvenir type copy. There is 0% chance that yours is genuine.

 

slap it in a slab by a professional indicting its real or not a copy. by going to any shop, imo, they can say anything they want or grade it anything that they want.
pony up the coin to get it graded, imo