I am always reluctant to assign attributions and I particularly like Welcome Mathewson's work. In fact, years ago I tried to buy his house. I've had a couple of his guns and probably examined as many as anyone. This gun does have certain features that he liked, although none of the are unique to his work. He favored a long wrist with an oval shape... it looked light from the side but was really quite thick. He also favored a long hand rail and the silver wire work is similar to his guns. But, the mounts are simply typical of lots of NE guns and are almost certainly imported. I know he bought English locks from a Providence hardware dealer and have seen some of the receipts (which are still in the possession of his family). They also have his rifle and his own fowler ... a London-made single barrel gun by Philip Bond.
I would give it a "guarded" attribution... The fact is, it could just as easily have been made by half a dozen other NE gunmakers. Also, If I remember correctly, he set up in business in 1805. His family also have his day book with entries for all his guns. Most aren't recognizable from his descriptions but I remember one "best finished rifle' that cost $25. The name of the purchaser was included and I've examined the rifle, with the owner's initials on the escutcheon along with a masonic device - all proper for NE at the time. The appendix to Achtermeier's book is a transcription of the day book. It is well worth studying in detail.
Mathewson did a lot of repair work... there are entries for things like "restocking one old soldier gun"... I have a really curious short musket. To look at it you'd think it was just cut down but the forend is relieved for a bayonet and there is a bayonet lug. Strictly speaking, it's a Dragoon Carbine as Dragoons were originally mounted infantry. RI had only one militia Dragoon unit and Welcomes brother was the Captain. The family still has his saber as well.
The barrel of my musket has Queen Ann proofs and the lock is quite similar to that on this fowler. It came from the collection of the late Dr. Louis Sage who lived in Coventry - next to Burrilville and was known for taking guns in trade for his services. Dr. Sage was in practice there from just before WWI to the 1970s and all his guns were acquired locally. But, I'm still hesitant to say Mathewson stocked the gun. It looks like he did but it isn't signed (nor would you expect it to be).