That could be a 1-3 Pfennig German States Coin from the 19th century up to 1870. Prissia, Hesse, Saxony would be most likely. These did look all very similar save for teh coat of arms.
Side note: It didn't become worn due to circulation. These are commonly called Pocket Pieces or Worry Coins. It was common at the time that men were told that so long as they have silver in their pocket, they will never be broke. These pieces would be pocketed everyday as if it was part of their morning ritual in getting dressed. The rubbing of the coin over years and decades would wear them smooth.
A piece such as yours would be priceless as it was likely your grandfather's pocket piece that your father kept. Hold on to it and hopefully, you can pass it on to your son.
I too have a pocket piece, or a WORRY COIN as I called it, an 1848 Large Cent, it's wearing smooth ever since my dad & I picked it up at a coin show back in the 60's. Normally got it out at funerals, weddings, etc., now I'll be giving it to my oldest grandson to pass it on.
Thanks guys. My family hasn't been good at keeping up with our history so to learn it was a "pocket piece" is neat. I am honored to have it. While I wish dad had told me about it, I bet you are right, it was likely my grandfathers on his side. He died before I was born and was in WW1 as I recall being told.