The Patriots were a group of individuals that saw themselves as freedom fighters, while portrayed as terrorists by the Republic. Basically, they were "rebels" of the Republic. They are only occasionally mentioned in Legend but have larger roles toward the end, as Kaede is revealed to be a Patriot and they help Day escape his execution.
The group was supposedly working for the Colonies in Prodigy. Their plan was to kill the Elector Primo, which was at this time Anden. Day and June attempt to sabotage the assassination attempt, but it is forced through by the Patriot's leader Razor. However, the plot fails, and many Patriot members are arrested while Anden escapes alive. It is later revealed that Razor was a double agent, secretly working with the Republic (and not the Colonies) to install himself as Elector Primo after Anden's assassination, as it is said that the Colonies knew nothing about Razor's plan. Tess also escapes with the Patriots out of anger at Day.
In Champion, some (possibly all) of the remaining Patriots have been captured but are shortly released. Pascao and Frankie have larger roles, and Tess is seen to still be working with them. At the end of the book, the Patriot group itself is not mentioned (although Pascao and Tess as individuals are) and it is implied that the rebel organization shut down, as the Republic actually had decent government now.
It is mentioned that similar activities to the Patriots are ongoing in Mexico, The Republic and the Colonies' southern neighbor.
Day (later left, then sort of re-joined)
June (later left)