Given the age of the piece I think it quite possible the poster does not have an American dime Well, not a new one anyway All I can say is that it does not appear to be British. Where was it found?
That must be a pretty early relic for America, then. It does look a bit too round for hammered. Some sort of early Spanish or Portugese copper?
Virtually any country's coinage was acceptable, some of it even US legal tender until 1857. From its weight relative to size it may be billon rather than coin silver and from what little design is left I think possibly a billon piece of the one of the German states, including Austria). I do not think it a hammered piece but one made from a screw press, typical of 18th century coinage. If it was found in what were once the Middle Colonies (NY,NY, PA, DE, maybe MD) the chance of it being one of the German states is quite possible from the large number of German immigrants to that region in the 1700's and of course the German troops brought over by the British during the Revolution.
Could possibly be Dutch. Look at late 17 and 18th c. coinage. Just a thought. Right now I'm puzzling out some Islamic pieces. Good luck, it's a nice puzzle.
There were quite a few German immagrants to Pa. in the colonial days and the remaining curved part of the design looks like Austrian types with curving elements....
The only really recognizable marker seems to be an "I"... closer look might be a "1/4" which could point to a badly damaged Swedish Skilling - late 18th century maybe? I don't think anyone else really did their 1/4's that way. I hope that helps.