Potent potions, which are dropped from slain monsters when Bastian Hallix is the player's active companion or without Bastian active if the player has unlocked Bastian's Julianos Medallion, state that they provide additional effects over normal looted potions. However, they do not. The additional effect does not appear on the character menu and does not affect the player's stats or tooltip power.
As these items drop at the player's level, there are multiple versions of these potions with different names based on the level when they were acquired.
Sip/Tincture/Serum/Dram/Effusion/Potion/Draught/Solution/Philter/Elixir/Panacea/Distillate/Essence of Potent Health states that it restores Health and Magicka and provides Major Fortitude and Major Intellect. However, the potion only restores Health and Magicka and provides Major Fortitude. These potions do not provide Major Intellect.
Sip/Tincture/Serum/Dram/Effusion/Potion/Draught/Solution/Philter/Elixir/Panacea/Distillate/Essence of Potent Magicka states that it restores Magicka and grants Major Intellect and Major Sorcery. However, the potion only restores Magicka and provides Major Intellect.
Sip/Tincture/Serum/Dram/Effusion/Potion/Draught/Solution/Philter/Elixir/Panacea/Distillate/Essence of Potent Stamina states that it restores Stamina and grants Major Endurance and Major Brutality. However, the potion only restores Stamina and provides Major Fortitude.
This is frustrating because Potent Magicka and Stamina potions are identical to ordinary looted potions--that is, Bastian basically provides no companion perk.
I have reported this issue using the in-game Help menu since 2021 and it remains unresolved.
As an aside, I would also recommend increasing the chance to loot a Potent potion; I have had Bastian's Julianos Medallion unlocked since late 2021, and I have about 200 of each potion collected total.