What is the value of an Indian head penny dated 1803 that is mounted into a round setting for a necklace?

Indian Head cents were minted only from 1859 to 1909 -- you must have something else.

I have one unmounted, found on an island beach in Chesapeake Bay. It is struck from sheet copper as a little "medallion" and, if unmounted, you would find it is indented in the back,from the striking die. Mine is dated 1803 as well. IOne archaeologist speculated that it may be commemorative for the Louisiana Purchase (1803) OR 15,000,OOO.

More information from others would be helpful to us both.

I also have an Indian head penny dated 1803. mine is mounted in a piece of wood on the top of an old looking pill box. I'm afraid I don't know anything more about it.

I suspect your "coins" were made by some private company for use in jewelry - or to decorate pill boxes/snuff boxes, etc. Value would be determined by what it is attached to, even if it were a real coin since collectors will consider it damaged once it has been mounted.