Being a relic-digger for 40 years, and having done micro-examination of many hundreds of corroded button-backmarks, there's a CHANCE that I could ID it from seeing just a few letters in the backmark. I cannot guarantee success at that... but please post some well-focused closeup photos of your button's backmark.
One thing I can say about its time-period without seeing the back:
It is a brass 3-piece button which has what button collectors call a "narrow" rim. In the mid-1870s (and afterward), many were produced with a "wide" or "extra-wide" rim. Therefore, your 3-piece button with the narrow rim is most likely from before the 1870s.
I should mention, there are two exceptions to that time-dating-by-rimsize rule. But your Massachusetts State Militia Staff-officer button is not one of the exceptions.
Compare the rim sizes on the New York Militia buttons in the photo below.
Button #12 has the wide rim,
#13 (your type) has the narrow rim,
#14 has the extra-wide rim.