definitely not the back of a button. I will post a pic below of the back.What does the other side look like? While I have never seen an example like yours I think what you are showing us is actually the button back. Unless, of course there is a loop on the other side. If that is the case I don't know what you have.
I was thinking the same, and thought possibly a saw medallion. And -Maybe- says Sheffield along the bottom?
The writing looks like it says "quality", does it look like that in person?

The writing looks like it says "quality", does it look like that in person?
When I mentioned possibly saying Sheffield I meant on the bottom beneath the bottom (of the circle) that clearly says Quality.It definitely says QUALITY on the bottom...

When I mentioned possibly saying Sheffield I meant on the bottom beneath the bottom (of the circle) that clearly says Quality.
Like this: View attachment 1517145
That image is from this site, which has a really impressive compilation of medallions: Saw Medallion Reference Guide - by summerfi @ LumberJocks.com ~ woodworking community
The medallion is from Turner Davies & Co.