In Baskerville's first season, 2018, he totaled 18 tackles, with 0.5 tackles going for a loss. In week four of the 2019 season, Baskerville blocked a punt and returned it for a touchdown; he also returned an onside kick for 46 yards as he helped LSU beat
Vanderbilt. Baskerville finished the 2019 season with 15 tackles, four being for a loss, a sack, a pass deflection, a fumble recovery, and a touchdown. In week ten of the 2020 season, Baskerville had a career performance tallying 12 tackles, one going for a loss, and a forced fumble, but LSU would fall to
Texas A&M 20–7. Baskerville finished the 2020 season with 55 tackles, 4.5 going for a loss, and a forced fumble. In week seven of the 2021 season, Baskerville recorded his first career interception, which he returned 54 yards, as he helped the Tigers beat
Florida 49–42. In week eleven, Baskerville had a performance that included racking up 12 tackles, 3.5 being for a loss, and two sacks, but LSU would lose versus
Arkansas. Baskerville finished the 2021 season with 83 tackles, nine going for a loss, two sacks, three pass deflections, and an interception. In week two of the 2022 season, Baskerville picked off a pass and returned it 29 yards for a touchdown, as he helped LSU beat
Southern. In week six, Baskerville had a career day, making 15 tackles against
Tennessee. Baskerville finished the 2022 season with 89 tackles, 4.5 being for a loss, one sack, eight pass deflections, one interception, and a touchdown. Baskerville finished his career at LSU with 260 tackles, 22.5 going for a loss, four sacks, 12 pass deflections, two interceptions, a forced fumble, a fumble recovery, and two touchdowns. ==Professional career==