Concerning the U.S. TV Westerns "Gunsmoke", "Have Gun Will Travel", "The Rifleman", and "Bonanza", the one that debuted first was "Gunsmoke". This TV series ran for 20 seasons from September 1955 to March 1975. It lasted for 635 episodes.

The first 12 seasons of "Gunsmoke" aired Saturdays at 10 pm, seasons 13–16 aired Mondays at 7:30 pm, and the last 4 seasons aired Mondays at 8 pm. All of the episodes were presented on the CBS Network. During its second season in 1956, the program joined the list of the top-10 television programs broadcast in the United States. It quickly moved to number one and stayed there until 1961. It remained among the top-20 programs until 1964.

"Gunsmoke " is a series that depicts life as it might have been in any U.S. frontier town. Dodge City, Kansas is a typical town of the late 1800s, with its share of saloon brawls, family arguments, bank robberies, and threats to law and order. Marshal Matt Dillon is there to keep the citizens safe, and the town as peaceful as possible. He doesn't reach for his gun as a first response; he solves crimes and disputes using judgement, clues, and keen observations. He uses cunning and skill to catch outlaws. When given no choice, he doesn’t back down. He’s quick to fight back and use his gun. He is fair, honest, and dedicated to enforcing the law in Dodge City.

The shows "Have Gun Will Travel", "The Rifleman", and "Bonanza" each debuted in the month of September in 1957, 1958, and 1959, respectively.

More Info: en.wikipedia.org