In his senior season, he was named Ohio Mr. Basketball[6] and made the Jordan Brand Classic, which was not played due to the COVID-19 pandemic.

On July 22, 2020, Branham committed to playing college basketball for Ohio State over offers from teams such as Alabama, Baylor, and Iowa.

[8] Sources: Branham started his college career off the bench, but quickly became a regular starter.

[9] He scored a career-high 35 points in a 87–79 overtime win against Nebraska after a nearly month-long COVID pause.

[16] In his Summer League debut, Branham scored fifteen points in a 99–90 loss to the Cleveland Cavaliers.