Third party is a term used in the United States for American political parties other than the Republican and Democratic parties.
What is a fourth party candidate supposed to be?
The Fourth Party System is the term used in political science and history for the period in American political history from about 1896 to 1932 that was dominated by the Republican Party, excepting the 1912 split in which Democrats held the White House for eight years. American history texts usually call it the Progressive Era. The concept was introduced under the name "System of 1896" by E.E. Schattschneider in 1960, and the numbering scheme was added by political scientists in the mid-1960s.1
I've read it in the following articles Third (and fourth) party candidates face challenges for exposure, ballot position , Why Not Third And Fourth Party Candidates For President?.
I can't seem to figure out, from the context what's meant by a fourth party candidate. I guess it's a kind of an overstatement for a candidate from a relatively small third party, as opposed to the bigger ones?