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From Marlin website:

How can I receive information on an antique Marlin Firearm?

Write to Marlin and give us all the information on the particular firearm, including model, serial number, caliber, barrel markings, etc. We will furnish general information on that model. If you would like specific Marlin (or L.C. Smith) serial number information, the Buffalo Bill Historical Center in Cody, Wyoming can research your serial number(s) for a fee (see below).
The old serial numbers are quite complete for the years 1883 to 1906 (serial numbers 4096 to 355,000), for the following models:
1881

1889

1892

1894

1897
1888

1891

1893

1895

1889 pump shotgun (serial #s 19,601 to 67,000)

In most cases the records include the model number, date of shipment from the factory, barrel length and type (round, octagon, etc.), and whether the stock had a pistol grip. They do not include to whom the gun was shipped. Extra features, such as checkering or engraving, are seldom listed. Serial number information for models other than those listed above are not available. Records after 1906 are not available.

The L.C. Smith shotgun records of the Hunter Arms Company, and for those manufactured by Marlin are also quite complete, and include more details. (No L.C. Smith information exists for any guns manufactured in Syracuse, NY).

When corresponding with the Buffalo Bill Historical Center, be sure to furnish as much pertinent information as possible about the gun (model number, serial number, patent dates, caliber, barrel length, etc.).

Cody Firearms Museum - Att:Marlin Records
Buffalo Bill Historical Center
P.O. Box 1000
Cody, WY 82414

We are confident that your dealings with the Buffalo Bill Center will be to your satisfaction.