What year was the model 34 16 gauge shotgun built it is a winchester red letter?

First I would check the model number of your winchester shotgun.The correct model number is 37.Winchester made the model 37 single shot from 1936-1963,with 1,015,000 made during this time span.Th red letter reference is only to the model 37 shotgun.While many of these were made over the years,Winchester never kept records on these shotguns because they were made with no serial numbers.A firearm serial number was only required after the gun control act was passed in 1968.