In his first nine games for Boise State, Jessup averaged 9.4 points per game. He scored 20 points in a win over
Presbyterian, becoming the 11th Bronco freshman to score 20 points in a game. Jessup's play drew comparison to former Boise State player
Anthony Drmic. “His feel for the game is so good, and he’s a worker,” coach
Leon Rice said. Jessup averaged 15.0 points per game in the first nine games of his sophomore season and led the team to an 8–1 start. Jessup was publicly reprimanded after his role in a court scuffle in a win against
New Mexico on February 6, 2018. He averaged 11.6 points per game as the second option behind
Chandler Hutchison and hit 46 percent of his three-point attempts. As a junior, Jessup led the Broncos in scoring (14.0 points per game), rebounds (4.5 per game), assists (2.7 per game), steals and blocks. Jessup was named to Third-Team All
Mountain West following his junior season. He played most of the season through knee pain and had surgery in April 2019. On December 7, 2019, Jessup set career highs with 27 points and seven 3-pointers, as Boise State defeated the
Colorado State Rams 75–64. Jessup made his 276th career three-pointer in a game against
UNLV on January 8, 2020, breaking
Anthony Drmic's Boise State record. He finished with 18 points to help the Broncos win 73–66. On February 4, 2020, Jessup broke the
Mountain West Conference record for career three-pointers when he passed
BYU's
Jimmer Fredette's mark of 296. At the conclusion of the regular season, Jessup was named to the Second Team All-Mountain West. He averaged 16.0 points, 4.4 rebounds, 2.1 assists and 1.4 steals per game. ==Professional career==