The Vishnu avatar linked to Balipratipada’s victory over Bali is Vamana.
In the best-known Vaishnava account, King Mahabali was a powerful and generous asura ruler who had conquered the three worlds. Vishnu appeared before him as Vamana, a dwarf Brahmin, during a sacrificial ceremony. Vamana asked only for as much land as he could cover in three steps, and Bali agreed.
Vamana then expanded into the cosmic form Trivikrama. His first two strides covered the realms under Bali’s control; when no ground remained for the third, Bali offered his own head. Vishnu therefore honored Bali’s devotion while sending him to rule Sutala, the netherworld. He also granted Bali permission to return to earth annually.
Balipratipada, also called Bali Padyami in several regions, commemorates this encounter and Bali’s generosity. It is not a story about Narasimha, Varaha or Parashurama; those are different Vishnu avatars with separate mythic episodes.