I assume this is an old Ithaca? The question didn't identify it sufficiently. Not sure about the "A" in front of the number, but Ithaca serial # 202454 should indicate a Flues/New Ithaca Gun model made in 1910. 410's are much rarer than 12 GA, for instance, so it will be worth more. A lot of the value depends on condition, and of course - if a collector is interested in that specific model. That being said, I suspect it could be worth in the $600-$800 range, based on what I see guns selling for at gunbroker.com. A gun dealer would probably have the Bluebook of Gun Values, and could pin it down more accurately. Good luck.
With the serial number that you provided,your Ithaca double barrel shotgun with the damascus barrels was produced in the year 1900.
1896
27p
Exactly how is the shotgun marked (all markings), and double-check the serial number. sales@countrygunsmith.net
Around July of 1925
1900
it is worth about 400 dollars
Impossible to answer without more information.
about 200.00
If it is a double, remove barrel and you will see it along with serial #.
That is impossible to determine without knowing the manufacturer and model of the shotgun.
You may have to break the shotgun down in to the barrel section and the receiver section first.Look under the barrel section on the flat just ahead of the lug for the serial number.