The mark would be under the date and it would be a proof coin. It can't get on the jacket, even on an error coin.
"It" didn't. A random blob did, as random blobs do on millions of other cents, and you're staring at random blob after random blob until you convince yourself that one looks like a letter or number. Besides, why are you ignoring the one-eyed zombie peering out from behind Lincoln's head? It's equally easy to see, and equally rare!
The S is exactly as "real" as the zombie, no more, no less. And it's no more or less significant. Look at it closely -- it's not an "S", it's a blob, like the one above Lincoln's head, with a dark curl coming off it at the top. Only when you look at it from a distance does it look like an S.
Actually they are saying you are experiencing pareidolia. It is not an illness, it is just a brain circuit that tries to make something out of randomness. Here is one page on it, you can search and find many more. It is common for people looking at high magnification of a small area. And the more they are getting frustrated , the harder their brains works to make sense of it. It is not a letter the mint put on it. Jim https://www.livescience.com/25448-pareidolia.html
The Face on the Moon and the Face on Mars are great examples if Paredolia - https://en.m.wikipedia.org/wiki/Face_on_Moon_South_Pole And https://en.m.wikipedia.org/wiki/Pareidolia