It is not a Model 1861, but rather a variation, called the Special Model 1861. They differ considerably from the standard Model 1861 in the contour of the hammer, the lockplate and the absence of a cleanout screw. Amoskeag never made the Model 1861. The original finish was bright, so the one pictured here has been blued, at considerable loss of value. The 1863 is the year of manufacture.
Other than the blue job and the stock break, the gun appears to be in fair shape, with the correct ramrod. In that condition, I would estimate a value of $1000 or so. In good condition with a whole stock, value could go close to $3000.
The Special Model of 1861 has been the subject of considerable speculation among collectors. The original contract with Amoskeag Manufacturing Co., of Manchester, NH, clearly specified an exact copy of the Model 1861. But Colt was making the Special Model, and somehow both Amoskeag and Lamson, Goodnow, and Yale (LG&Y) ended up making the Colt-type gun rather than the 1861.