Yours is a much rarer version of NY York State Militia Officer button. (The more-common version shows a small eagle perched on a globe atop a large shield, whereas yours has a large eagle with a shield on its chest showing parts of the New York State Seal.) It is shown as button NY-28-A, B, or C. (I can't quite tell from your photo whether it is version A, B, or C.)
You did not say anything about your button having a backmark. I need to see it's back to time-date it. It's back is particularly important, because if it has a self-shank back, it is from the early-1900s and is not a Military button -- being instead worn by civilian New York State Government officials.