Here is a link to an auction site that sold a similar piece, at least mentions "Anderson, Texas". They suggest that it was manufactured by “Blunt and Syms of New York”. Researching that manufacturer may help.
“This is the so called 'Anderson' underhammer pistol that many think was made in Anderson, Texas. This piece functions well even though the main spring is just a little weak. This piece has been cleaned slightly but isn't as shiny 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.”