The gun appears to be similar to a Allen & Wheelock Single Shot Centerhammer Muzzle-loading gun.
Looking at the photo of one of these in the FLAYDERMAN'S GUILD TO ANTIQUE AMERICAN ARMS, 9th edition, page 68, the trigger guard is not the same and the buttplate on the gun in the book's photo has a deep curve to it, typical of the guns made in the 1850's. Also, the wrist of the stock on your gun seems to extend up at least half way to the receiver frame.
The book says this about the gun they show:
"Single-Shot Muzzle-Loading Center Hammer Percussion Rifle by Allen & Wheelock. (a.k.a. "No 10 Inside Cock"). Made c. 1850's. Quantity unknown, very limited.
Amde in various calibers and barrel lengths. Also made as a smoothbore shotgun.
Irono mountings; lock-casehardened, the barrel browned. Wooden ramrod beneath barrel.
Walnut buttstock with crescent shaped buttplate; no forestock. Stock sual; earlier production had narrow iron forend.
Serial numbered. Barrel marking: ALLEN & WHEELOCK.
A distinctive feature is the center hung hammer slightly offset to the right to allow for sighting, and the long integral iron frame extending, full length of the wrist. Rare."
Does your gun have a metal buttplate at the rear of the stock or has it been cut off leaving nothing but wood? I can't tell from your pictures.