If a spell is played through Fizz's triggered ability and it is countered, does it still get recycled?

Yes, if a spell is played using Fizz, Trickster's ability and is subsequently countered, it is still recycled.

According to RiftJudge FAQ #10401, this occurs because Fizz's ability creates a replacement effect that applies whenever the spell would leave the chain for any reason. This replacement effect overrides the standard rule (Rule 425.1.a) that a countered spell is sent to the trash.

The Sequence

1. Playing the Spell: When Fizz's "When you play me" (WYPM) triggered ability resolves, you play the spell from your trash.
2. Replacement Effect: Because this spell was played via Fizz's ability, the instruction "Recycle that spell after you play it" applies to it. This creates a replacement effect that monitors the spell's movement from the chain.
3. Countering: If an opponent plays an effect (such as Defy) to counter the spell, the spell is normally cleared from the chain and sent to the trash.
4. Resolution: The replacement effect from Fizz's ability activates, replacing the "send to trash" event with a "recycle" event. The spell is moved to the bottom of the owner's deck instead of the trash.

This is an explicit exception to the general rule that countered spells are sent to the trash (Rule 425.1.a, Rule 156).