Yes, you read that correctly back in 1851 a three cent piece was minted. Postage rates had gone down from 5 cents to 3 cents giving people the ability to have a single coin to make small purchases with. The coin was smaller than our current dime and was minted from 1851 - 1873. They were made of silver but also included with cooper so folks wouldn't melt them down for their silver value.
There were two different three cent pieces. The three piece silver and the three cent nickel. The later was produced during the Civil War to help stop the hoarding of silver coins. The nickel was produced from 1865-1889.
You can read more about this at Wikipedia
A three cent piece became the discussion of politicians again in 1911 but that isn't our century of focus.
You can also do a search at Google books and come up with several references of three cent pieces. Along with the "Laws of the United States relating to loans, paper money, banking, and coinage, 1790 - 1895. In there you'll find the percentage of metals to use to produce the coin.