If I attack with Green Yasuo and he gets stunned, does his ability damage still go off?

Yes, if you attack with Green Yasuo and he becomes stunned, his "When I attack" ability damage still resolves.

According to the Riftbound rules and FAQs:

• Stun only prevents combat damage: Rule 410.1.b states, "A Stunned Unit does not contribute its might to damage in combat." It does not prevent the resolution of triggered abilities.
• Ability damage vs. Combat damage: Ability damage and combat damage are distinct. Stunned units are still capable of triggering their abilities and dealing damage through those effects.

Sequence of events:

1. Attack Trigger: When Yasuo is moved to attack, his "When I attack" ability triggers and is placed on the chain.
2. Stun: If Yasuo is stunned (e.g., by a reaction or effect) after the trigger is placed on the chain but before it resolves, the stun does not remove the ability from the chain.
3. Resolution: The ability resolves, and Yasuo deals damage equal to his Might to the target.
4. Combat: During the combat resolution phase, the stun will prevent Yasuo from contributing his Might to combat damage, but the damage from his ability has already been dealt.

This is consistent with the ruling in FAQ #7935: "Yes, a stunned Yasuo still triggers his 'when I attack' ability and deals his might damage. Combat damage and ability damage are different, and stun only prevents combat damage."