The Rochester Jeffersons from Rochester, New York played from 1898 to 1925, including play in the American Professional Football Association/National Football League from 1920 to 1925.
Formed as an amateur outfit by a rag-tag group of Rochester-area teenagers after the turn of the 20th century (a 1925 report has the team being founded in 1898), the team became known as the Jeffersons in reference to the locale of their playing field on Jefferson Avenue. Around 1908 a teenager by the name of Leo Lyons joined with the club as a player, and within two years began to manage, finance, and promote the team on a full-time basis. For their first decade of their existence the "Jeffs" played other amateur and semi-pro teams from the upstate New York area such as the Rochester Scalpers and the Oxfords. From 1914 to 1917, the team grew stronger with opponents from Buffalo and Syracuse. In 1916, they were the New York State champions. By 1917, the Jeffs had started to look past state borders not only for big-name opponents, but for big-name talent as well.
At the end of October 1917, Lyons managed to secure a match against the country's greatest team, the Canton Bulldogs, who had the legendary Jim Thorpe as their star attraction. Thorpe's squad crushed the Jeffs 41–0, but the audacity of challenging such a superior team to a match won Lyons and his club a bit of notoriety. In 1920, Leo Lyons was at the Hupmobile showroom in Canton, Ohio to become an original member of the newly formed American Professional Football Association, which would be known in two years as the National Football League. The NFL recognizes that 1920 meeting as the founding of the National Football League.
The team ultimately did not win a single game in its last 23 games played in the APFA/NFL. The team had 5 different coaches in its five seasons in the NFL making this arguably the worst or most dysfunctional franchise in the early years of the NFL. They are also known as the first team to allow 50 points in consecutive games in 1923. This only happened once since by the Chicago Bears in 2014.
Sources
https://www.pro-football-reference.com/
https://www.profootballarchives.com/index.html
https://americanfootballdatabase.fandom.com/wiki/Football_Wiki
https://www.gridiron-uniforms.com/GUD/controller/controller.php?action=main
https://www.profootballhof.com/hall-of-famers/
Bob Carroll, "The Town That Hated Pro Football,". Pro Football Researchers Association, Coffin Corner: Vol. III, 1981.
The Official Rochester Jeffersons Website
The history of the Arizona Cardinals is extraordinary compared to most franchises in the NFL. The Cardinals compete in the National Football League as a member of the league’s National Football Conference West division. The Cardinals were founded as the Morgan Athletic Club in 1898, and are the oldest continuously run professional football team in the United States. The team was established in Chicago and was a charter member of the NFL (APFA which the league was called its first two years) in 1920. Along with the Chicago Bears, the club is one of two NFL charter member franchises still in operation since the league’s founding, the other being the Bears (back then known as the Staleys). The club moved to St. Louis decades later in 1960 and played in that city through 1987 then moved to Phoenix. 
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