Then I'll continue my guessing - it must be something big, so I'll hazard Kubilai Khan (and if so, I'll be incredibly envious...)
It appears to be a 3-cash coin cast under Kublai Khan. Inscription reads "Je Üen Tung Baw" in Mongolian, and "Zhi Yuan Tong Bao" translated to Chinese. Rated as a 2 on the Hartill scale, meaning it is quite rare (for reference, H-19.15). Just out of curiosity, where did you get it? EDIT: I was looking at the wrong line. Rarity 6, not 2.
The thing that worries me that it is just soo nice. Also, I cannot find another example where the bottom character is written the way it is, with the top stroke not being inscribed all the way to the left. I am certainly no expert to later cash coins (and having been burnt on two Yuan pieces does not help) and I could be completely wrong, but this coin does not have the "feel" of a Yuan-Dynasty coin. I need to study this a bit more. Some examples: https://www.zeno.ru/showgallery.php?cat=6861 http://db.stevealbum.com/php/lot_auc.php?site=1&lang=1&sale=24&lot=881 Being purchased from a reputable dealer is a big plus, but that does not ensure authenticity, unfortunately. The fakes are just too good. And I apologize if I make you worry too much about your new (?) coin. The fabric is similar to a fake I own, though mine is a bit cruder in execution.
Your other example is a perfect example of what one of these should look like. https://www.cointalk.com/threads/mystery-coin-of-the-day.260545/
Yours is closest to this one, but that nefarious top stroke... https://www.zeno.ru/showphoto.php?photo=20888
I believe the stroke is fine. One cannot refute the fact that something smells fishy. I have searched high and low and cannot find a match real or fake. Looking at your "fake" the similarity seems superficial and it is quite crude, but comparison is noted.
"For the price I paid for it - that would be stupid unlikely. Not impossible, just stupid unlikely." That is an important piece of the puzzle when trying to figure out it's authenticity...and please don't mention what you paid, that is your business. I often try to flip the script on these things. Can you prove it is legit? Not trying to be a you know what, what I am saying is that it's your coin that you purchased. If I said it was fake, what would you point to in order to refute that claim?