You will probably need a well-informed collector of early Colt revolvers to definitively identify this piece. Cartridge conversions of the Colt percussion revolvers were very common during the post-Civil War era, with 1860 Army .44 revolvers and 1851 Navy .36 revolvers converted to either rim-fire or center-fire cartridge use by several commercial gunsmithing companies (of varying reputations and skills). Colt offered their own conversions, then produced the transitional Model 1871-1872 "open top" revolvers as a factory-produced product rather briefly just before the new Single Action Army model was introduced in 1873.
What I see in the photos appears to be a transitional piece with the cylinder either modified from percussion to center-fire, or perhaps manufactured for cartridge ammunition, frame including a loading gate, and an extractor/ejection rod added to the barrel extension to facilitate cartridge use. The hammer (when retracted for cocking) will reveal either a center-fire type firing pin or a rim-fire type striker, and that will help to identify the era of manufacturer or modification as well as the producer.
Steel grip-frame and trigger guard tells me it is most likely a factory-produced variant. Caliber will help in differentiating between the various models, with .38 being most common for the Navy variants and .44 more common for the Army variants.
Grips appear to be well-aged ivory done as "one-piece" type, more typical of factory production than of the various conversion gunsmithing operations of that era. Ivory one-piece stocks are a very, very desirable collectible in and of themselves.
With the little information retained in my head, I am leaning toward either a Colt factory conversion, or an early transitional "open top" factory piece. Overall proportions, particularly the length of the grip-frame, lead me more toward the .44 Army type than the smaller .36 Navy variants, but the differences are difficult to tell from the photos. The revolver appears to be complete and functional, with all visible serial numbers (barrel group, frame, trigger guard) appearing to match, which would probably indicate a factory-produced "open top" model.
Definitely time to consult an expert on this one.