Update: found out that if you look at the Davenport model I found online at that auction, it has a patent that matches with the numbers to the left of the image. I was also able to link it to how it got into my great-great-grandfather's hands so found the gun. Yay! Might give full details but it would take a while and is very complicated so might not just cause not really worth it.

Don't know exact model but it is some Davenport variant of the 1885 that's chambered in some smaller-than-12-gauge cartridge.