Does ward trigger if the spell targeting the permanent is a copy created by Fork?

Ward (CR 702.143) triggers whenever a permanent with ward becomes the target of a spell or ability an opponent controls. The trigger checks whether the permanent is being targeted, not how the targeting spell came to exist. A copy of a spell created by Fork (or Twincast, Reverberate, etc.) is a new independent spell on the stack (CR 706.10), and if that copy targets a ward permanent, ward triggers separately for that copy.

This means if an opponent casts Lightning Bolt targeting your creature with Ward 2, ward triggers once. If you then Fork that Lightning Bolt and the copy also targets the same creature, ward triggers a second time — requiring the Fork's controller (the opponent) to pay an additional 2 life or the copy is countered. Each targeting event is evaluated individually.

CR 706.10 is key: 'A copy of a spell is itself a spell.' Because the copy is a real spell on the stack with its own targets, all game rules that care about spells targeting — including ward — apply to it fully.

Example: Your opponent controls a Goblin with haste and casts Reckless Charge targeting your Aether Channeler (Ward 2). They also Fork the Reckless Charge, with the copy targeting the same Aether Channeler. Ward triggers twice. Your opponent must pay 2 for the original and 2 for the copy (total 4), or whichever trigger they don't pay for results in that spell being countered.

Confidence is HIGH: this follows directly from ward's definition in CR 702.143 and the rules on spell copies in CR 706.10, with no known exceptions.