I have found the enhanced petri's philter, but I can't find the basic recipe. I would assume it's from a merchant, but I've checked most.
I found a recipe for Petri's Philtre on the first floor (up the ladder), at Drahim Castle, in Velen.
From the pictured Quick Travel point, walk towards the left of the castle. You will see a doorway that can be broken with Aard or sword. Walk through the doorway, and climb up the ladder found within. The formula is in a lootable box near the next ladder up.
This is likely one of many locations to find this formula, and it's possible that it was a randomly generated loot item.