Serial numbers started with UL tags. Only UL Listed stoves (not yours) will be dated.
Some fabricators stamped, others wrote in weld on the bottom a "stove number" in order of fabrication.
Most had their own way of marking for warranty purposes.
I can tell you the year or very close with pictures of the front by the spring handles and draft caps among other things. Leg style (taper or angle) helps identify where the stove came from as well as weld around vent pipe. Each fabricator had their own way of doing things that I've documented over time.
The first double door stoves were Bicentennial with '76 on the right front door in a star. Early 1977 still had the star with no '76 on the star. These use a round door seal rod instead of flat channel iron found on all later stoves. In 1977 optional bolt on shields were added to revised drawings sent to fabricators. Shields were added when not used on a non-combustible hearth. This designated them as a II. 1979 started optional "Cathedral" arched top doors along with the old style flat tops. These were designated III. They are not marked on the stove, but the drawings show the Roman Numerals as well as the manuals. 1980 discontinued the flat top doors. 1980 also started a new design for the box, eliminating the angle iron corners. These stoves had bent corners and were the UL Listed stoves with integral shields that could not be removed. The double door UL Listed III stoves also incorporated the Smoke Shelf Baffle. (The single door stoves were not III, they were VI due to glass double door version being IV). There was no V. What makes it confusing is many fabricators continued to make the old style Un-Listed style for $100 cheaper for use on non-combustible hearth where a shielded UL Listed stove wasn't necessary. So you go by the door style to confirm before or after 1980 when you have angle iron corners. Before 1980 were many changes to springs, draft caps and door handles to date them, after 1980 the caps, springs and handles on the arched top doors stayed the same, so are not capable of dating unless someone has a receipt or it is a PA stove that was numbered on the bottom since the original customer list still exists at the existing Fisher Stove Factory Showroom in Factoryville PA.
Also look for an "H" stamped on the front and center of ash fender channel iron trim.
The first post of this thread gives more details of the changes listed above;
https://www.hearth.com/talk/threads/fisher-grandma-and-grandpa-bear-details-fireplace-series.69448/