The letter on your "button" is an Old English Script (not Manuscript) letter W. Note the two narrow vertical bars in between the three main "arms" of the W. You'll see the W in the diagram attached below.
The reason I put quotation-marks around the word "button" in my first sentence is, your find never had a button-loop or shank. The large wide-open round hole in its back indicates it is either a rivet-button or snap-closure, missing some of its components. It could have come from a garment like overalls, a denim jacket, or a pants-waist closure.