That is a fairly rare "SMALL FRAME/SMALL BORE HAMMER GUN". These were made from 1909 up to around 1921 (last catalogue entries.) 1st issue was in .44 shot shell (.44-40XL shot and Marble .44 Gamegetter with shot capsule) and 28 gauge. Later 20 ga. was added and .410-44 replaced the .44 shot.
The through bolt has been replaced with one that has a square nut on the right side. Originally these were cut to exactly fit from side plate to side plate and thread into the right plate. It is a true sidelock with individual fire control systems contained in each lock. The hammers are driven by coil springs and spring guide, not flat or V springs as is common for that era.
Your pictures are not real clear on my screen - the wear on the furniture is extreme but it 'seems' to be original configuration.
There were only about 5000 pieces made during the production life. Rumor is that this model originated in Belgium and that H&R purchased the design and manufacturing equipment and brought it to the US to set up the line. At the time this model was introduced, H&R was making three single barrel shot guns in two frame sizes (1900 with removable hinge pin and 1908 with snap off forearm - both large frames, 1905 small frame.) Previously, H&R had produced under license, the "ANSON & DEALEY" hammerless gun - from around 1880 to 1884. These were the first hammerless guns made in the US and just about the most expensive shotgun of the period, made in 5 grades. These are now collector items and sell up to $2K+.
The Model 1909 SF/SB hammer guns are highly collectible today, in good to excellent collection they sell at retail for $600 to $1000+, respectively.
In the condition your gun is in, it is still worth a couple hundred bucks mostly as a parts gun.
I purchased a GOOD .44 ss for $800 and a 28 ga in high V.GOOD condition about 8 years ago for $1000. I haven't seen many sold on the major on-line auction sites, since I bought mine - but the last one I did see sell went for about $1200.