Chris Paul had the most games with 20+ assists and exactly 0 turnovers, with 1 game.

most games with 20 assists and 0 turnovers
Interpreted as:
most regular-season games by a player with 20 or more assists and 0 turnovers
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NAMEGPASTTOVMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINPTSREBSTLBLKPF+/-
Chris PaulChris Paul120029.820.05.020.03.00.00.08.016.050.03.06.050.01.02.050.030205303+21
StatMuse has game-level data for turnovers going back to the 1984-85 season.