Barron needed 75 stitches to close a cut after he fell onto the skate of Vegas Golden Knights goalie Laurent Brossoit during a net-front scramble in Game 1 of the 2023 Western Conference First Round. He did not miss a game; the Jets lost the best-of-7 series in five games.
Selected by the New York Rangers in the sixth round (No. 174) of the 2017 NHL Draft, Barron has 27 points (11 goals, 16 assists) in 102 regular-season games for the Jets and Rangers.