I have two Bay State banjos: a 300 and a 318. John C. Haynes Company was a leading musical instrument dealer in Boston in the 1890s. Bay State Banjos were manufactured after the Excelsior lion, I believe. As far as I know, there are no serial numbers. The mdoel numbers do not have much consistency, and the peghead, neck scale length and inlays, and pot size can vary widely. For example, my 318 has a fiddle shape peghead and rather fancy inlays. Bernunzio had a 318 with a scroll peghead and dot inlays.

Model 300 was the bottom of the line, and the numbers run up through the 350s and maybe 360s. There are Bay State catalog reprints available for sale, though they provide only a little guidance since the models varied so widely.

I enjoy playing my Bay States. They are not so highly values as an S.S. Stewart, but the quality is similar in the low and mid-range instruments. The banjos are not as common as Stewarts or Dobsons, and the lack of consistency in the models may hurt their "brand." Depending on the condition, your 301 may be worth $200 to $600. If it's an 11" pot with all-original hardware, a straight neck with nice inlays and in playable condition, it may be worth $500-700 to some. Replacing the friction tuners with modern geared tuners will make it more playable but probably hurt its value. Friction tuners, new or old, work well with nylon or Nylgut strings which is probably what it should use to avoid damaging the neck.

I think you may have a nice banjo there.