A Parker Bros. shotgun with serial number 63849 would be from about 1890. The only way to know for sure would be to order a research letter on the gun from the Parker Gun Collectors Association -- http://www.parkergun.org
Unfortunately it appears there web site has been down since Friday. Once it come back up, don't just jump on the forums and start asking questions. First read all the information available there. They have sections on markings, grade identification, etc.
In 1890 Parker Bros. hammerless doubles were offered in 8-, 10-, 12-, 14-, 16-, and 20-gauges and in at least six grades. Parker Bros. hammer doubles were offered in both the older lifter-style openning and the top-lever style openning, the same six gauges and even more grades. We need a lot more information and several good pictures to figure out what you have and even get in the ball park of a current market price.
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