You have an H&R Model 1900, stamped for catalogue, hardware store and wholesale sales as the "BAY STATE" aka "a BRAND NAME" shotgun. It is a very late Model 1900, as this model was discontinued circa 1916-'17. This is the earliest example of a "BAY STATE" stamped shotgun that either Bill G. or I have encountered. It pushes the production period of the Brand Name pretty far back. Bill's research indicated that the first catalogue (dealer's) mention of the Bay State was in the 1932 price list.
Bill theorized that the name Bay State was first used by Hopkins and Allen when they purchased the "BAY STATE ARMS Co. / Uxbridge Mass. sometime in the late 1890's, early 1900's. H&A sold out to Marlin Rockwell circa 1917 - which means H&R may have adopted or purchased the name around then. If true - your Bay State would be one of the first H&R produced pieces with that name. That's about it for the history. Bad news is that the Model 1900 (of which your gun is a variation) was chambered for 2 1/2" shells during most if not all of it's life span. You need to get the chamber depth checked before you shoot anymore 2 3/4" shells - no sense bursting anything on that gem. Also, the metal used (called semi-steel) for the receiver is a bit soft and a lot of shooting of smokeless powder shells (earliest Model 1900 were equipped with either fluid steel or "layered Damascus type" barrels) may deform the hinge and locking lug latch-up. BE CAREFUL. I've found the EJECTOR on this model (came as ejector or extractor) to be quite robust.
The vast majority of this model, that I've seen, anyway, have been marked CHOKE on the top of the barrel - so I'm guessing what passed for a full choke back then is what you can expect to see on your gun.
TO REMOVE the hinge pin: raise the toggle; turn it approximately 1/4 turn either right or left until the lug fits the keyway and then it will pull straight out. The gun will then be field stripped to it's two main components. The forearm is removed by turning out the screw on the underside.
Good luck! Any pics? Especially of the left side of the receiver? Also, there should be a serial number on the rear tang of the trigger guard? Will you share it? These guns were serialed along with the parent model and having one of this fairly well established age/ YOM, will help settle some s/n to year questions?
NICE FIND and thanks for sharing. PICS please!!