This looks to something of a military nature. It has what looks to be two spots on the backside where metal hooks or posts may have been. Found at an old homesite. What is it?
Due to the object's size (in relation to the coin shown in the photo), and having two spots on the back where a metal bar was broken off, it isn't a button, it is a horseharness rosette. Specifically, it is a US Army horsegear rosette from 1902 into the 1930s, showing the Great Seal of the United States. Here's a photo showing the backside of an intact one, and another photo showing one on a horseharness "headstall."