Found in Irithyll of the Boreal Valley.
From Central Irithyll, make way past the plaza with the fountain. To the left of the second Fire Witch there will be a small terrace with a Crystal Lizard. The banister on the right is illusory and will reveal a staircase once hit. Head down the stairs past a Pontiff Knight and toward a cell with a deranged Evangelist named Dorhys inside. The staff lies next to a tree on the right.
The primary strength of the Witchtree Branch is that it maximizes the casting speed of the player upon wielding it, making it unnecessary to use the Sage Ring and thus allowing for other rings to used. This even applies to a catalyst being wielded in the opposite hand.
However, this comes at the cost of having the worst Spell Buff out of all staves in the game, regardless of the amount of Intelligence that the player has leveled. As such, this staff is best suited for casting non-scaling utility spells such as Snap Freeze or Aural Decoy.
Reinforced with regular Titanite.