Welcome to the forum and thanks for posting.
You have 1st Model SMALL FRAME HAMMERLESS 1st Variation made circa 1899-1903.
The last patent date which apparently is partly unreadable on your piece should read:
APR.7.'96. It is suitable for BLACK POWDER loads, only. Serial number range on these seems to extend from 01 to approx. 82,000, so, depending upon your serial number the exact year can be estimated.
The "standard" issue for this variation is: 3" barrel, Nickel plate, 5 shot .32 S&W (the short one) and molded, black hard-rubber grip panels. Options include: barrel lengths of 2" (BICYCLE model), 4", 5" or 6" (the longer barrels are scarce); polished blued finish and grip panels of M.o.P., checkered walnut and (very rare) Ivory.
The RETAIL valuation for this model, currently: 100%/NIB $225; 95% $195; 90% $155; 80% $130 - all prices quoted are +/- $20 depending upon area.
This black powder model seems to have been fairly well received and approximately90,000+ were produced before H&R switched production features to handle smokeless/Nitro powder versions in 1905.
The small button on the left side of the top strap will hold the barrel latch in an upright position (for removing and reinstalling the cylinder) if pushed in while lifting the latch and then let go once latch is in raised position.
Here's a pic of a couple of pieces from my collection.