Though the character was created by the Coens in The Big Lebowski (1998), it was John Turturro who came up with Jesus's eccentric personality and mannerisms.
The Coens' only involvement is giving John Turturro permission to use the 'Jesus Quintana' character.
In the article from "Corrections Today" (the front page that's framed in the warden's office) it says: "Millionaire Jeffrey Lebowski sponsored the Sing Sing Black Sheep's bowling team providing equipment and uniforms and players to tutor them in fundamentals. He helped coach them the first season.".
The film carries a 2017 copyright date, indicating it was completed two years before release.
Movie is based on the book "Les Valseuses" and leans heavily on the look of the 1974 movie Going Places (1974) based on the same book.