Is mine with a factory 2-1/2" barrel a sherrif or storekeeps model? Where is the S located?
The problem there is yours, like the one posted by Dingus above, requires a factory letter to prove it to be, or not to be, a storekeepers or sheriffs. It could very well be a storekeeper/sheriff, and it may not be as well. To be 100% sure requires a factory letter and anything else is a guess unless verified by an expert like Kopec (would still back up a Kopec letter with a factory to be 100%).
It's also worth mentioning that some nefarious individuals in the lifetime of the gun may have altered the Colt very convincingly in the pursuit of financial gain, and to do so they may have gathered and used period correct frames and parts. Who know's what's happened in the lifetime of that Colt (not saying that's what anyone here has done for the record). If spending the extra amount to aquire, or reallly just looking to keep a good investment around, it's worth having the factory letter.
Im not sure on the 1877 DA thunders if they stamped them with and S or not. Im still researching mine theres also a double inspectors mark in the hammer well on mine the big C which is the right inspector for 1877 made SAA Colts but mine has a tiny 0 to up above the C so its intresting it should only have the C not the 0 as well. the S on mine is on the back end of the frame where the back strap attachs to the frame just below the screw hole. yours looks to be a sherrifs model to me. im no expert on DA thunder Colts tho or there markings.
I have a SAA colt with LAS stamped on it its a factory SAA colt conversion to 22 magnum has LAS who was a Inspector in the 1940s so the other gun i have was a factory conversion.
the markings on colts are intresting. i have a list of all the inspectors and when they worked at Colt.
I always take the trigger gard and back strap off to check if the loading gate number matchs the number stamped under the trigger gard on the frame thats how i found the markings on my sherrifs model. tho alot were made from regular SAA BP framed colts to so you have to be carefull. i dont care either way as im keeping mine there so nice to point and shoot being so light weight.
I'm going through my reference material and have to say that it would be news to me that a "S" has any meaning toward sheriffs model. Don't get me wrong I could be learning something new here, but this is the first I've heard of it and it's not documented anywhere I can find. Mind sharing your reference please? Would love to learn something new and maybe add a new anecdote to the antique database with your permission

(after verification of the meaning of course).
At the moment it's seeming much more likely to have been a inspectors mark after re-inspection that has been worn down with multiple refinishes possibly wearing off the rest. Those patent dates are worn, and it looks like there could be remnants of the tip of the US martial marking near the patent dates. A worn down inspectors mark in this case shouldn't be ruled out.
The "C" could also mean condemned. At the moment I'm not aware of an inspector with a single C marking in 1877 making condemned parts likely, but of course this could require more research. That would in any case be a unique place for an inspectors mark, or the condemned mark.
How blunted from the refinish is the frame serial numbers? It'd be interesting to know if it has inspectors marks or if they were perhaps removed with a refinish, which would be a shame.
Of course if you have a factory letter saying it's a sheriffs or storekeeper then you know beyond a shadow of a doubt

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