Georgia hasn’t had any party (other than the Democratic and Republican Parties) on the ballot, with its party label, in a regularly-scheduled U.S. House election, since 1942. But all other states have had such minor party candidates on the ballot for U.S. House during the 21st century, if the year 2000 is deemed to be in the 21st century.
The last minor party on the ballot for U.S. House in Georgia was the Independent Democratic Party, which was on the Georgia ballot in 1940, 1942, and 1944. Back then, Georgia permitted two parties to jointly nominate the same candidates. The Independent Democratic Party was a conservative party, and it cross-endorsed the Republican presidential elector candidates in Georgia in 1940 and 1944, but it also ran its own nominees for other partisan office, including U.S. House in both 1940 and 1942. Before 1943, Georgia let any party on the general election ballot with no petition. Starting in 1943, Georgia required a petition signed by 5% of the registered voters, unless the party had polled at least 5% for the same office in the previous election. The Independent Democratic Party was on the ballot automatically in 1944 because it had polled more than 5% for President (for Wendell Willkie) in 1940.
Georgia’s imposition of the 5% petition has been fatal for minor party candidates for U.S. House, in the 70 years that requirement has existed. Under Williams v Rhodes, which struck down Ohio’s old ballot access law in 1968 because it hadn’t been used successfully for five presidential elections in a row, the Georgia requirement ought to be held unconstitutional, because 35 elections have been held and it has never been used for U.S. House. The 5% standard for statewide office was lowered in 1979 and again in 1986, but the Georgia legislature has never amended it for U.S. House.