Patterson was considered among the top 5 high school class of 2016 football prospects in the entire country.

[12] Patterson enrolled early at the University of Mississippi (Ole Miss) and was tabbed as the second quarterback on the depth chart, along with second-year freshman Jason Pellerin, going into 2016 fall camp.

Patterson made his debut on November 12, 2016, leading the Rebels to a comeback victory over Texas A&M while completing 25 of 42 pass attempts for 338 yards, two touchdowns, and an interception.

[15][16] The following week, Patterson earned his second career start, against Vanderbilt, and completed 20 of 42 pass attempts for 222 yards and two touchdowns during the Rebels' 38–17 loss.

Before the season began, Ole Miss was mired in controversy due to an NCAA investigation that found numerous violations of organization rules, including a lack of institutional control.

[18] In another controversy, Ole Miss head coach Hugh Freeze resigned in July 2017 after it was reported that he made several calls to escort services using university phones.

In the first two games of the season, Shea garnered national attention by throwing for a combined 918 yards and 9 touchdown passes against South Alabama and UT Martin.

[22] After the conclusion of the 2017 season, it was announced that Ole Miss would be banned from the postseason again in 2018 due to the NCAA violations.

Patterson sought a waiver in order to be eligible for play immediately at Michigan, claiming that he had been misled by Ole Miss coaches during his recruitment regarding the ongoing NCAA investigation.

[29] Following the loss, Patterson's fortunes improved along with the rest of the Michigan team, as the Wolverines won the following ten games and rose to fourth in the College Football Playoff rankings.

In a 45–20 victory over SMU on September 15, Patterson posted a career high in passer efficiency rating (232.3) to go along with 237 passing yards, two touchdowns and an interception.

[30][31] On November 3, Patterson threw two touchdown passes and ran for another on the ground in a blowout 42–7 victory over then-No.

[32] He was named Big Ten Player of the Week by the Rose Bowl Game Football Committee following the win.

[33] In a regular season-ending loss to rival Ohio State that knocked Michigan out of contention for a Big Ten title, Patterson threw for 187 yards, three touchdowns, and one interception.

[34] In the Peach Bowl against Florida, Patterson posted a season-low in passer efficiency rating (114.2) as he threw for 236 yards, one touchdown, and two interceptions in a 15–41 loss for the Wolverines.

[38] After a bye week, the Wolverines were soundly defeated by Wisconsin on the road, 35–14; at points, Patterson traded snaps with backup Dylan McCaffrey.

[42] On November 23, in a 39–14 victory over Indiana, Patterson threw for 366 yards and five touchdowns, becoming the first Michigan quarterback with consecutive 300-yard games since Jake Rudock in 2015.

[49] Patterson signed a contract with the Texas Rangers that allowed him to play out his final two years of eligibility at Michigan, while not appearing in any minor-league games during that time.

On May 3, 2020, he signed with the Kansas City Chiefs where he joined former Michigan quarterback Chad Henne and former Ole Miss teammate Jordan Ta'amu as backups to Patrick Mahomes.

[59] Due to injuries to Vernon Adams and Matthew Shiltz, he dressed in 5 games as a short yardage quarterback and rushed for 18 yards on 11 carries.

His older brother, Sean, was an associate player personnel analyst with the Ole Miss football staff.