Haven't had a lot of luck with it. The style of it looks Roman. But the composition is brass. The profile seems to have waving/flowing hair which doesn't quite look Roman and why I had the idea maybe pre or post colonial America. The reverse is more flat. The obverse is thinner on the outer part. The profile is raised and thicker than the edge. It also does seem partially eroded whether this was from being buried or done chemically. I haven't had much hope showing it to local dealers either. The letters on the reverse are well defined.
Over an hour later and nothing found so far. Just added a few lines ...
On reverse not sure what the standing figure is holding in right hand.
Also looks like a curved bow as well. No idea if any of that will be on the
actual coin when someone finds out what a better example looks like.
I may find the holy grail before I solve the mystery of this coin. It could be nothing phenomenal like a replica of some sorts. But it seems like it has a story to be told. Even with a magnifier and good light the letters aren't more legible expet the ones on the right of the standing figure. I wondered if it could be some early USA token with the flowing hair resembling Liberty on some early 19th century American coinage. The figure on the reverse could be a depiction of a native American.
I looked very hard at a U.S explaination for your coin. Early tokens, State Coppers, etc. in Redbook and elsewhere and it has many features similar to a bust right Connecticut copper and even the reverse figure is very similar but it is definitely not a Connecticut copper or a variety of it. The one thing I am fairly certain of is that it resembles a George II and George III bust. As mentioned above, possibly minted in the UK for somewhere else in the Empire. I am leaning against a replica.
I think it is a Roman Provincial coin. The hole on the reverse seems to indicate as such as well. The legend seems to be Greek/Roman lettering. The obverse seems to be Herakles in lion skin, similar to below:
It is slightly like this coin - which further down the page has nice descriptions. https://www.ebay.com/itm/323867794300
and is nearly the same size as your coin.
Elagabalus Ancient Nicopolis Roman Coin w/ Athena Serpent Erichthonius
On reverse the tree in brown and snake in pink ...
But yes a different coin, and some lettering different. Though still similar design.
Obv: Laureate, draped and cuirassed bust of Elagabalus right.
Rev: Athena standing left before serpent coiled around olive tree to left; shield on ground behind her.