Gold coins of the United States were first struck at the Philadelphia Mint in 1795. Production of the gold coins was legislated by the Mint Act of 1792 which authorized the ten dollar Gold Eagle, five dollar Half Eagle and the Quarter Eagle whose denomination you would be correct in assuming to be two dollars and fifty cents. So, you see it took a few years before the gold Half Eagles and Eagles were struck, followed by the $2.50 gold Quarter Eagles in 1796. Gold coins were produced in the U.S. more or less continuously until 1933 at the Philadelphia Mint and also at mints in Dahlonega in Georgia, Charlotte in North Carolina, New Orleans in Louisiana, Carson City in Nevada, San Francisco in California, and in Denver, Colorado.
During that period of time there were six denominations of the United States gold bullion coins. By face value they are the twenty dollar Double Eagle containing one ounce of pure gold, the ten dollar Eagle with one half ounce of gold, the five dollar Half Eagle, the four dollar gold Stella (for the 5-pointed star on its reverse), the three dollar gold piece, the $2.50 Quarter Eagle, and last but not least the Gold Dollar weighing in at one-tenth of an ounce of pure gold. The Gold Dollar was produced in three design types from 1849 to 1889. Type I was struck from 1849 to 1854 and is known as the Liberty Head. Type II is the Small Head Indian Princess and was minted from 1854 to 1856. Then from 1856 until 1889 the Type III Gold Dollar was produced and is called the Large Head Indian Princess.
The two dollars and fifty cents valued gold Quater Eagle was produced during the years from 1796 to 1929. During that time there were eight major Quarter Eagle design types. One of the original authorized gold coins, produced only in 1796, is named for its having ‘No Obverse Stars’. From 1796 to 1807 was the Capped Bust, Stars type. The 1808 gold dollar coin type is called Capped Bust to Left. The years 1821 to 1827 saw the production of the type known as Capped Head to Left, Large Diameter, Stars Around Head. The 1829 to 1834 type is the Capped Head to Left, Smaller Diameter, Stars Around Head. From 1834 to 1839 look for the Classic Head type. The Liberty Head gold dollar was minted from 1840 to 1907. And the Indian Head is the type produced from 1908 to 1929.
The minting of $3 Gold Pieces took place in the years from 1854 to 1889. 1879 and 1880 were the only years when the $4 Gold Stellas were produced. The five dollar denomination Half Eagles were minted from 1795 through 1929. Ten dollar Gold Eagles were struck between the years 1795 and 1933. And the period 1849 to 1933 saw the minting of the twenty dollar Gold Double Eagles.