Which game mod directly inspired Teamfight Tactics?

Teamfight Tactics was directly inspired by Dota Auto Chess.

Dota Auto Chess was a custom game mod for Dota 2 that popularized the modern auto-battler format. Players assembled teams of heroes, placed them on a board, and watched rounds resolve automatically while making decisions about purchasing, combining, positioning, and upgrading units.

Riot Games responded to that rapidly growing genre with Teamfight Tactics, adapting the formula to League of Legends. TFT replaced Dota characters with League champions and built its own systems around traits, items, shared unit pools, rounds, and a rotating cast of themed sets.

The answer is not Defense of the Ancients, even though Dota Auto Chess was made for Dota 2, which itself descends from the broader Warcraft III custom-map tradition. Hearthstone Battlegrounds and Auto Chess Mobile are related auto-battler titles, but they were not the direct inspiration identified for TFT.