"El Paso" is a country and western ballad written and originally recorded by Marty Robbins.

"Out in the West Texas town of El Paso,
I fell in love with a Mexican girl.
Night-time would find me in Rosa's cantina;
Music would play and Felina would whirl."

Marty Robbins' 1959 album Gunfighter Ballads and Trail Songs features his hit "El Paso", similar in form and content to "The Streets of Laredo". The 1960 follow-up More Gunfighter Ballads and Trail Songs has a version of the original.

"As I walked out in the streets of Laredo,
As I walked out in Laredo one day,
I spied a young cowboy, all wrapped in white linen
Wrapped up in white linen and cold as the clay."

The old-time cowboy Frank H. Maynard (1853–1926) of Colorado Springs, Colorado, claimed authorship of the revised "The Cowboy's Lament", and his story was widely reported in 1924 by the journalism professor Elmo Scott Watson. (Source; Wikipedia)

There are several threads on Mudcat discussing the relationship of "The Streets of Laredo" to "The Unfortunate Rake" [Roud 2] and its wide family of songs.

"As I was a-walking down by St. James's Hospital,
I was a-walking down by there one day,
What should I spy but one of my comrades,
All wrapped up in flannel, though warm was the day."

"The House of the Rising Sun" is often considered another branch of the family and was, of course, a hit for the Animals in 1964. In that case, Alan Price was the lucky person who received the publishing royalties.