The Liberty Head twenty-cent piece was followed by the Seated Liberty twenty-cent piece, which was minted from 1866 to 1874. This coin featured a seated figure of Liberty on the obverse and a wreath of wheat on the reverse.
The next twenty-cent coin was the Trade dollar, which was minted from 1873 to 1885. The Trade dollar was intended for use in international trade, and it featured a depiction of a seated woman representing Liberty on the obverse and an eagle perched on a rock on the reverse.
The final twenty-cent coin minted by the United States was the Washington quarter, which was first minted in 1932 and is still in production today. The Washington quarter features a portrait of George Washington on the obverse and an eagle in flight on the reverse.
So, to answer your question, yes, the United States has produced several different types of twenty-cent coins throughout its history.