A guard from Savannah, Georgia, Quarterman attended Sol C. Johnson High School. As a senior, he averaged 19.5 points, 6.2 rebounds, 5.1 assists and 3.4 steals per game, leading the Atom Smashers to the Class AAA state title.
College career
Quarterman came to LSU in 2013. He was a starter for the Tigers as a sophomore and junior and averaged 8.4 points, 3.9 rebounds, 3.1 assists and 1.04 steals in 98 games. As a junior, Quarterman averaged 11.2 points, 4.6 rebounds, 3.6 assists and 0.97 steals in 33 games and following the season, he declared for the 2016 NBA draft.
After going undrafted in the 2016 NBA draft, Quarterman joined the Charlotte Hornets for the 2016 NBA Summer League. On July 25, 2016, he signed with the Portland Trail Blazers. Quarterman made his NBA debut on November 9, 2016 in a 111–80 loss to the Los Angeles Clippers, recording four points and one rebound in six minutes off the bench. In the Trail Blazers' regular-season finale on April 12, 2017, Quarterman scored a career-high 10 points on 4-of-11 shooting in a 103–100 loss to the New Orleans Pelicans. During his rookie season, Quarterman had multiple assignments with the Windy City Bulls and Long Island Nets of the NBA Development League, pursuant to the flexible assignment rule.
On June 28, 2017, Quarterman was traded to the Houston Rockets in exchange for cash considerations. He was waived by the Rockets on October 13, 2017. On January 2, 2018, Quarterman signed with the Jiangsu Dragons of the Chinese Basketball Association, but due to visa issues, he was replaced on the roster before appearing in a game. In February 2018, Quarterman joined the Agua Caliente Clippers of the NBA G League, averaging 8.9 points in 11 games. He signed with the Houston Rockets on March 30, only to be waived on April 12 after seeing action in three games.
On November 22, 2018, Quarterman signed a one-month contract with Ironi Nahariya of the Israeli Premier League. He parted ways with Nahariya on January 1, 2019, after appearing in three games. He averaged 5.0 points, 4.0 rebounds and 3.7 assists in 24.0 minutes per game.
On April 8, 2019, Quarterman signed with the Super City Rangers for the 2019 New Zealand NBL season. He parted ways with the Rangers on June 29, 2019. In 15 games for the Rangers, Quarterman posted averages of 28.1 points, 5.6 assists and 5.5 rebounds in over 36 minutes per game.
