You can see that the 'extra' S is not the same shape, or depth, as the normal letter on the edge. What you have are contact marks that look like an "S". If there were two "S's, they would look exactly, or almost exactly, the same. Your extra letter doesn't look like the normal letter; it's not an error, sorry to say.
I will post more pics of the coin . S isnt the only letter doubled . Every letter is doubled . I will try to take the best pics
There were doubled edge lettering on the Adams Presidential dollar, both overlapped and inverted. I have one of each along with one that has the edge lettering missing completely. I would have to see more pictures to say one way or the other.