A widowed homesteader raised his son on a New Mexico ranch and helped the local sheriff battle desperadoes using a modified Winchester rifle. The series aired during the heyday of the Western on network television. During the 1958-59 season, this show's first, the genre accounted for seven of the Top 10 shows. `The Rifleman' ranked fourth, below `Gunsmoke,' `Wagon Train' and `Have Gun, Will Travel.'