This link and information is from an auction site that makes referrence to a similar piece and suggests it was a "Blunt and Syms of New York pistol". Researching that manufacturer may help. It is a large page with many photos and takes a minute or two to load. Do a search on the page for "underhammer" and it will take you to the entry
"This is the so called 'Anderson' underhammer pistol that many think was made in Anderson, Texas. This pice functions well even though the main spring is just a little weak. This piece has been cleaned slightly but isn't as shiney as my pic shows. The wooden bag grips is missing a chip in one that you can see in the pic. There is engraving on the frame and on the top of the barrel is marked 'Cast Steel' 'Pocket Rifle'. There is provisions on the grip to use a shoulder stock of some kind. This piece has the 4 inch barrel being part round/part octagon. The saw-handle grip is all steel with walnut grips. See in Flayderman's 9th Edition page 423 7E-001.5 image. Flayderman's also states that these pistols are very similar to Blunt and Syms of New York pistols and strongly suggests that they are made by that firm."