I will offer another theory. I can't find a photo of the real ones, and my book is on loan, but they use to make coin theme bridle rosette and conchos, some of which had lead/solder backs, even though they were post Civil War. Below are reproductions of some of them. Your find may be the solder that has fallen out of one of the coin themed rosettes.
I would want it to be silver for you mostafa, but I agree with Smokey, I've never seen an American coin "squish" for wear like that, which would make a person think it is not a real coin at all, but perhaps a copy? made of a softer metal, as lead has been offered?, so, the size, thickness, weight might give you answers. Regardless, welcome to the T-Net from wherever your detecting from.
What you have is very likely a crudely made “fantasy coin”. There is no US dollar with that reverse design, so you do not have a federally issued coin. The reverse bears a resemblance to the heraldic eagle seen on Kennedy half dollars. Your coin was probably struck by an amateur diemaker who wanted to create a made up coin design.