You may find the date of manufacture by going to savage99.com This should give you the info that you seek.
check out www.savage99.com
Contact Savage Customer Service through their website.
Your Savage was made in the year 1937 if you have a model 99 lever action rifle.
You should contact Savage arms directly,they should identify the year of manufacture for your rifle.
If we are talking about a Savage model 99 rifle,chambered in 300 Sav. caliber,then your lever action rifle was produced in the year 1949 by Savage arms Company.
Riverside Arms was a name used by J, Stevens Arms and Tool Co (which became part of Savage Firearms) between 1915 and 1940. There are no public records for dates of manufacture.
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Your savage model 1899 rifle was made by the savage arms company in 1901 with the serial number 15779 that you provided.
Your Savage model 99E was made from 1960-1982 by Savage arms company.As to the exact year of production,you will have to contact Savage directly.
You will have to contact savage arms directly to get the answer to your question.
If your rifle is a lever action?Then it is a model 99 savage and with the serial number you provided it was made by savage arms company in 1921.
I can say that the Savage model 775 was made from 1950-1965.You may want to try Savage Arms companys home page and see if you can get a certain year of production by your serial number.