The short answer is you can not. There are no known company records for these guns. However, the chambering gives a clue. From about 1900 to 1915 they were chambered for 44 shot. In 1916 that changed to 410-44. Note the 44 is the 44XL / 44GG. Do NOT fire a 44-40 with a normal load in this gun. They changed the chambering again around 1920 to 410. The model 1900 and later 1905 were tremedously popular. In the course of 5 years, Harringto & Richardson had to expand the factory 3 times to meet the demand.
how to remove and replace trigger guard on Harrington Richardson topper shotgun n
1940's
How much is a 60 year old Harrington & Richardson Handy Gun, 410 gauge worth?
About $100.
How old is my Topper 88 HARRINGTON AND RICHARDSON GUN serial number
1940's
50-150 USD or so
Blue Book of Gun Values
The Harrington Richardson 20 gauge single shot shotgun, Feb. 27 1900 is valued at $75 in poor condition. In good condition, it is valued at $200.
1901 single barrel shotgun, washingtion
value of a harringtonand richardson 1900 28 gauge
Immediately after 119437.