You are the best Cannonball guy! I’m glad to know what the button is depicting because it looked like a very mean weird looking dog to me. Thanks for the link to the site as well.Iron Patch is correct, your find is a Livery button, made in Britain.
For anybody here who doesn't already know:
"Livery" buttons bore the symbol of an Aristocracy or (sometimes) a Nobility family, and occasionally a non-Aristocracy but extremely wealthy family. Most of the Livery buttons found in the US are British-made. As Smokey indicated, most of them date from the first half of the 1800s. The buttons were worn on the uniform of the family's household staff, such as butlers, coachmen, etc.
CoilyGirl, your button shows a mythological animal called a Wyvern, which was somewhat like a dragon. I could not find an EXACT duplicate of it at the Livery Buttons Identified website (link is below), but I do have a very close match to it in the Livery Buttons section of my computer's relic-images folder. I'll attach a copy of it at the end of this post. It's emblem is reported to be for the Rowley family.
Here's a link to a good website for identifying Livery buttons. The page at the link shows the "Dragons & Wyverns" category. On the left of that page, you'll see a very lengthy list of other Livery emblems, with their Family connection when that is known.