I'm probably gonna look like a fool here, but I'll take a stab at it.
Sometime around the end of the civil war, or shortly thereafter, the Govt. took some old Springfield muzzleloader rifles and converted them to breachloaders, what is now known as a trapdoor Springfield. I believe it used a paper cartridge, which was inserted at the breach and when the trapdoor was closed it clipped off the end of the cartridge, which created a primer charge. I really don't know how it was ignited. I really don't know much of anything about them, to be honest, I'm just guessing.
Any military arm the Govt was using at that time was a heavy caliber, 50 cal, give or take, so that's not what you have. My best guess would be that some gunsmith, copying the Springfield conversions, took a .30 cal squirrel rifle and converted it to a breachloader.
Ok, now everybody go ahead and laugh. I'm probably full of baloney, but I don't see anyone else making a guess. I've never seen a trapdoor Springfield, but I bet that's what the action looked like.
Dang thing might be worth a small fortune, or it might just be a conversation piece.