While it has similarities to a Stevens pocket pistol , I believe it is a " Parlor Pistol" designed to fire a very low power cartridge in either 4 or 5MM. Called Floberts
I think this is less likely than what I hypothesized. Parlor pistols are normally longer, and the mechanism of a top break WITH an automatic extractor (the extractor pushes the shell out upon opening of this gun) is unlikely to be found on a parlor pistol, or any pistol designed for indoor shooting. Parlor pistols normally have a swivel breech, or a type of modified rolling block, with a hammer, or some other type of primitive system, rather than a top break mechanism. The top break with auto extractor was current technology in those days in a single shot self contained cartridge pistol. Between its size, the fact that its top break, and the auto extractor, it only makes sense to be a pocket pistol with a SD purpose in mind.
Looking at the size of the pistol grip, and the length of the barrel, I don't think shooting it indoors with powderless flobert rounds would be enjoyable unless you were trying to shoot a door or a large wall.