That's Jackson, the county seat of Breathitt County, right? That area of southeastern Kentucky, in the Cumberland Plateau "hill county" region, had a number of gunmakers...but many of them didn't sign their work, so it is difficult to know for sure who made rifles coming out of that area. Until a signed or initialed rifle shows up to provide clues about a given maker's work, the work remains anonymous. Please check the top barrel flat several inches behind the rear sight for any trace of a name or initials...if anything is there, we may be able to figure out who made the rifle. The barrel appears rusty, but rubbing that area with a soft erasure will remove some of the rust without damaging the barrel, and allow a better view of the barrel surface where initials might be located. Also important is to ask the granddad who had the rifle, if there is any family history, or provenance, behind the rifle, and does he know if it originally came from Breathitt County, etc. Any information on the rifle's earlier life might help in identifying it.
The best known maker of Breathitt County was John B. Haddix. He worked there from before 1830 until after 1850 [census data]. If your rifle was made in that county, it would have been in the late 1830s or early 1840s, based on what I can see of the stock architecture and butt profile. The fact the gun has a curly maple stock, brass butt plate with a normal length "return" at the top, and non-exaggerated toe on the butt all suggest this is a KY gun, and not a TN gun. The parallel incised lines at the base of the cheekpiece, rather than converging lines, also suggests KY as the origin. The side facings, or narrow border of stock wood around the edges of the lock plate, are relatively uniform all the way around the lock plate mortise, again suggesting this is a KY rifle...TN rifles often had side facings [wood borders] that were wider at the front and rear of the lock plate than along the top and bottom edges.
The only known/identified gunsmiths working in Breathitt County at the time your rifle was made were: 1) John Haddix 1830-1850 +/-, and 2) John Back 1810-1854. There may have been another one or two, but if so, so obscure that they do not appear in any period records as a gunsmith. Two later Breathitt Co. gunsmiths, Wilson Montgomery and Larkin Norris, worked too late in the percussion era to have made this rifle. Keep in mind, even if used in Breathitt Co., the rifle could have also been made in a near-by county...by a totally different gunsmith. The barrel looks somewhat short for a KY rifle made in this area of KY in the 1830s or early 1840s. Could you help me better understand this rifle by providing the following additional pictures and measurements:
1. good picture of the rear ramrod pipe
2. good picture of the full tang at the back/breech of the barrel
3. good picture of the toe plate on bottom edge of butt at the rear
4. good picture of the rear and front sights
4. length of barrel, also approx. bore size measured across widest part of bore to the closest 32nd of an inch, such as perhaps 11/32" for example.
Again, please closely inspect the top flat of the barrel, several inches behind the rear sight, for any trace of a stamped or engraved name or initials...those would really help the search for the gunmaker.
Shelby Gallien