You have found a tea set that is American made. The maker's mark, the unicorn, is the mark of Mauser Manufacturing Co. They were in business in New York from 1887 through 1903. The "serial number" could be either an actual serial number, but is more likely a pattern number, showing that each piece is part of that set. If you want to verify that the mark is Mauser, go to the Encyclopedia of Silver Marks website and look up the Mauser mark. I suspect that it will match up.