You have a replica of a "Colt 1860 Army Revolver".
It is one of the "Four Screw" versions and the bottom of the metal grip strap should have a notch machined into the bottom at the rear of it.
The "forth screw" is the fillister head screw located on both sides of the frame above the trigger guard. Its purpose was to provide an attachment location for a removable shoulder stock which also clamps into the machined notch on the bottom of the grip.
The Model 1860 Army was the first .44 caliber gun made by Colt after the three models of Dragoon pistols.
The 3rd model Dragoon .44 was made from 1851 thru 1861.
The Model 1860 revolver was made from 1860 thru 1873. 200,500 were made with about 156,000 of them being made between 1860 and 1865.
This was the first model with the "creeping loading lever" and the stylized lower barrel lug, the earlier Colts using a link to operate the loading lever and having a much blunter more utilitarian barrel lug.
Although the grip looks much like the grip on the Colt 1861 Navy the grip and the rest of the gun is larger.
The engraving on the cylinder of the Colt 1851 Navy, the Colt 1860 Army the Colt 1861 Navy was the battle scene depicting the Texas Navy fighting the Mexican Navy.
The scenes on other Colt pistols range from a stagecoach holdup thru Dragoons fighting Indians.
These engravings were used by Colt to let his customers know they had a genuine Colt product. In fact several of his ad's tell prospective customers to look for the engraving for the proof of authenticity.
When Colt came up with the .36 caliber 1851 model it was first called an "intermediate" pistol but Colt (some say) changed the name to his "Navy" pistol. He also rather unsuccessfully tried to sell these to the Navy. They were widely bought by the civilian population and by the time the Colt 1860 Army was developed the Naval Battle scene was widely known. This possibly explains why the Naval Battle scene was used on the 1860 Army pistol.
As was mentioned, your cylinder has a step in it making what is known as a "rebated cylinder". This allowed the large .44 caliber to be used in a smaller, lighter frame without compromising the cylinders strength. Prior to this model, the .44 Walker and the three models of .44 caliber Dragoons had a straight cylindrical cylinder and a much larger frame. They were much heavier than the 1860 Army. (over 4 pounds unloaded).
The Army had been using .44 caliber Colts from before 1849 and felt the caliber was more suited for bringing down horses. Colt, understanding this chose the .44 caliber for this new Army revolver.
I'm sure you will enjoy your pistol. If you plan on shooting it it will use .451 or .453 diameter lead roundballs. Any real "black powder" or a black powder substutite like Pyrodex will work and it will need #11 percussion caps. Under NO circumstances should a modern smokeless powder of any kind be used in your pistol. Smokeless powder will blow your gun up.
The ball size suggested is larger than the chambers and a thin lead ring will shear off of the balls as they are rammed into the chambers. Many folks put a layer of grease or vegetable shortening over the top of the ball once seated to lubricate the bore.
Have fun