2010-11: John Quenneville appeared in two minor midget AAA games with the SSAC Bulldogs — skating most of the season with the SSAC Lions bantam AAA team — and played for the Edmonton South Bruins in the Alberta Cup. He scored 1 goal with 3 assists with the Bulldogs. In 33 bantam AAA games he scored 35 goals with 40 assists and had 52 penalty minutes. Quenneville had 2 assists and 6 penalty minutes in five Alberta Cup games. He was selected by Brandon in the third round (54th overall) of the 1011 WHL Bantam Draft.
2011-12: Quenneville skated in 11 junior A games with the AJHL's Sherwood Park Crusaders alongside his older brother Peter Quenneville (CBS) and played for the midget major SSAC Athletics. He had 3 assists in nine regular season games for Sherwood Park and scored 2 goals in two playoff games. He scored 15 goals with 18 assists and had 40 penalty minutes in 30 AMHL games with the Athletics. Quenneville skated for Team Alberta in the Western Canada U16 Challenge Cup; finishing with 5 assists in four games.
2012-13: Quenneville made his WHL debut as a 16-year-old — skating in 47 games for Brandon — and represented Canada Pacific in the 2013 U17 World Hockey Challenge. He scored 8 goals with 11 assists and was -18 with 14 penalty minutes on a Wheat Kings team that finished last in the East Division. Quenneville had no points nor penalty minutes in four games at the WHC.
2013-14: Quenneville had a breakout season in his second year with the much-improved Wheat Kings. Led by Quenneville and fellow 2014 draft prospect Jayce Hawryluk, Brandon was leading the East Division after January and both were scoring at a point per game pace. Quenneville scored 21 goals with 24 assists and was -7 with 45 penalty minutes in his first 45 games. He was ranked 34th amongst North American skaters in Central Scouting's mid-season rankings prior to the 2014 NHL Draft.