Particularly given the Forsyth County, Georgia, provenance, your rifle is undoubtedly by Philip Bettis who worked in Forsyth County. I have seen several of his rifles, signed "P Bettis". Here is the information on Bettis published in GUNSMITHS & ALLIED TRADESMEN OF GEORGIA, by Wayne Elliott and James Whisker:
"Bettis, Philip (1836-). gunsmith. 1860, Cumming, Forsyth County, Phillip Bettis, 25, blacksmith, born in S.C.; Matilda Bettis, 25, born in N.C.; Gibbs Bettis, 2, born in. GA; William Davis Bettis, 1, born in GA. 1870, Vickery Creek District, Cumming, Forsyth County. Phillip Bettis, 34, m, w, gunsmith, value of real estate $250, value of personal estate $500, born in SC; Matilda Bettis, 37, f, w, keeping house, b. NC; all children born in Georgia: Gibbs Bettis, 13; William Bettis, 11; Toliver Bettis, 6; Eliza Bettis, 9; Lenora Bettis, 4; Victoria Bettis, 4. 1879, Vickery’s Creek [State Dir]. Philip Bettis, 44 gunsmith; Matilda, 49. 1881-82, Vickery Creek, Forsyth County [U.S. Census]; Dir]. Several P Bettis rifles are extant."