Hello!
The basilisk tooth is an extremely rare reward that can only be found on one specific path. It can only be found on Route A (the sequence of events that happens if you accept Zenaida's contract in the tavern at the Docks - if you decline her contract or do not visit the Docks at all then you are on Route B and there is no opportunity to retrieve the tooth). Your character must also be half-melusine.
During the confrontation with the Count, you need to be knocked into the water and then fight the basilisk below the surface. Successfully passing the Strength or Perception checks OR failing the Strength check (which will result in an injury) will allow your character to kill the basilisk and retrieve the tooth.
There are multiple versions of fighting the basilisk but this is the only one that will result in retrieving a tooth.






