[6] In 2016, he played for the Greensboro Grasshoppers of the Single–A South Atlantic League where he started 24 games, pitching to a 4–9 record with a 2.91 ERA, and in 2017, he pitched with the Jupiter Hammerheads of the High–A Florida State League and posted a 3–7 record with a 4.16 ERA in 16 games (14 starts),[7] earning All-Star honors.

[8] In 2018, he played with both Jupiter and the Jacksonville Jumbo Shrimp of the Double–A Southern League, pitching to a combined 4–15 record and 4.98 ERA over 26 games (25 starts) between both teams.

[9] He returned to Jacksonville to begin 2019,[10] where he was named an All-Star,[11] and was promoted to the Triple–A New Orleans Baby Cakes of the Pacific Coast League in June.

[15] He made his major league debut that night as the team's starting pitcher versus the Arizona Diamondbacks, and picked up the win after pitching five innings, giving up two earned runs.

[22] Poteet spent the majority of the 2023 season recovering from surgery, and made one scoreless appearance for the Triple–A Omaha Storm Chasers.

[30] Poteet made 5 appearances (4 starts) for the Yankees, logging a 3–0 record and 2.22 ERA with 16 strikeouts across 24+1⁄3 innings pitched.