Like most songs on Dylan’s debut, this is his interpretation of a folk standard. This one was first recorded by Blind Willie Johnson in 1927.

The liner notes of Bob Dylan reveal that the first time Dylan performed this song was when he recorded it for the album:

Dylan had never sung “In My Time of Dyin'” prior to this recording session. He does not recall where he first heard it. The guitar is fretted with the lipstick holder [makeshift slide] he borrowed from his girl, Suze Rotolo, who sat devotedly and wide-eyed through the recording session.

https://www.youtube.com/watch?v=t5HaHVKRouo

Led Zeppelin performed their own version of “In My Time Of Dyin'” on Physical Graffiti.