Yoshimo's Companion Quest - Baldur's Gate 2
Yoshimo technically has 2 Companion Quests for you to complete, the first of which starts when you visit Docks District for the first time. Upon entering the Docks District Yoshimo will tell you that he needs to speak with Renal Bloodscalp who is a member of the Shadow Thief Guild. You'll find the Shadow Thief Guild in the northwestern portion of the Docks District.
Renal Bloodscalp will start the quest chain, Find Proof of Mae'Var's Treachery. That's all Yoshimo's first Companion Quest is, directing you to speak with Renal Bloodscalp so you can start this quest chain. Having Yoshimo with you doesn't change the quest at all outside of some additional dialogue with him and Renal.
As for Yoshimo's second quest, this begins only if you bring Yoshimo to Spellhold with you during Chapter 4. When you're at Spellhold during Chapter 4 Yoshimo's treachery will be revealed to you and you'll be forced to end his life before you escape Spellhold.
When Yoshimo dies in Spellhold one of the items he'll drop is Yoshimo's Heart. This item can be turned into any Temple of Ilmater in the game and purified which will net your party 200,000 EXP in total. While this does seem like a lot of experience you should keep in mind that it will be split amongst your entire party.
You can find a few Temple of Ilmater's in Athkatla, the one I typically visit is the one in the middle of the Slums District.