[4] As a true freshman, Ossai played in all 14 of the Longhorns' games with two starts and made 20 total tackles with one a sack and a forced fumble.
[5][6][7] He led the team with 62 tackles in his sophomore season while also recording five sacks, two interceptions, one pass broken up, one forced fumble and also blocked a kick.
[10] On 14 December 2020, Ossai announced his decision to enter the 2021 NFL draft, choosing to forgo Texas' 2020 Bowl game and his senior season.
[20] He appeared in 16 regular season games and recorded 3.5 sacks, 17 total tackles, one pass defended, and two fumble recoveries.
[21] In the AFC Championship Game against the Kansas City Chiefs, Ossai committed an unnecessary roughness penalty with eight seconds left in regulation on quarterback Patrick Mahomes resulting in a 15-yard penalty and much closer field goal attempt (45-yards) which kicker Harrison Butker converted to advance to the Super Bowl.
He recorded one deflected pass, his first 2 career forced fumbles, career-highs in sacks (5), tackles (26), TFLs (4) and QB Hits (15).