Law of the Plainsman

The series recounts the exploits of Sam Buckhart, born among the Apache Indians but eventually educated at Harvard University and now a Deputy U.S. Marshal in the New Mexico territory of the 1880's.
He is training under Marshal Andy Morrison in Santa Fe, living in a rooming house run by Martha Commager along with an orphaned 8-year-old girl he rescued. The Buchhart character originated in two episodes of The Rifleman: The Indian and The Raid.