If it says 32 Winchester CTG on the barrel, that would be a 32-20 Hand Ejector Model of 1902 second model if that is the correct serial number. 1903-1904 is the correct time frame for that number, but it should be a 4 screw, not a 5 screw. It should be a round butt K frame gun.
Pics would help tremendously in correctly identifying what you have.
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