Jefferson spent his true freshman year at Arkansas in 2019 as a backup to Nick Starkel who lost the starting job to SMU transfer, Ben Hicks.[7] He made his first career start against LSU.[8] He finished the season, completing 14 of his 31 passes for 197 yards with one interception and also rushed for two touchdowns before redshirting.
As a redshirt freshman in 2020, he was the backup to Feleipe Franks. He appeared in five games and made one start for an injured Franks.[9] He finished the season completing 20 of 41 passes for 295 yards, three passing touchdowns and two rushing touchdowns.
Jefferson entered the 2021 season as the starter.[10][11] Jefferson started all twelve games for Arkansas, helping the Razorbacks finish the season 8–4 overall record, and 4–4 in SEC games. This included a non-conference victory over Texas, and trophy game wins over Texas A&M (The Southwest Classic), LSU (Battle for the Boot), and Missouri (Battle Line Rivalry). It was the first time in team history that Arkansas had won all three trophy games in the same season. Jefferson started for Arkansas in their season-ending Outback Bowl game versus Penn State, and led the Razorbacks to a 24–10 victory, and a 9–4 final record. Jefferson was named the Outback Bowl MVP. His final season statistics after the bowl game were 2,676 yards passing for 21 touchdowns and only four interceptions while completing 67.3 percent of his passes for a QB efficiency rating of 164.7. He also rushed 146 times for 664 yards and six rushing touchdowns, all team highs.
Jefferson was again Arkansas' starting quarterback in 2022, starting twelve of the Razorbacks' thirteen games. He led Arkansas to an overall record of 7–6, 3–5 in SEC play. Four of Arkansas' six losses (Texas A&M, Liberty, LSU, Missouri) were by a grand total of nine points. Jefferson sat out the LSU game due to injury. He guided Arkansas to their second straight bowl victory, beating Kansas in an exciting 2022 Liberty Bowl, 55–53 in 3OT. Jefferson was named the Liberty Bowl MVP, completing 19 of 29 passes for 287 yards and two touchdowns, and rushing for 130 yards and two rushing touchdowns on 14 carries. He finished the season with a QB efficiency rating of 165.2, slightly better than the previous season.
Jefferson returned to Arkansas for his redshirt senior season in 2023. He would go on to pass for 2,107 yards, 19 touchdowns, and 8 interceptions while running 161 times for 447 yards and 2 touchdowns. His 8 interceptions marked the highest of his career, and he posted the lowest completion percentage, passing yards, completions, yards per attempt, and touchdowns since he became the starter in 2021. The Razorbacks would finish the season 4-8 and miss out on bowl eligibility for the first time since 2019.
On January 1, 2024, Jefferson announced that he would be transferring to UCF.[14]
Jefferson was benched during the 10/12/2024 game against Cincinnati and remained benched for the 10/19/2024 game against #10 Iowa State in favor of sophomore Miami transfer Jacurri Brown.
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