What magic powers did the trident of King Triton have?

Answer 1

I assume you are referring to King Triton in Disney's "The Little Mermaid"?

Aside from being a rather threatening weapon King Triton's trident is shown to have several magic powers. He is able to emit energy from it in order to destroy the human artifiacts Ariel has collected as well as a statue of Eric, her soon to be boyfriend.

Later in the film he tries to use a similar power to destroy the contract made between Ariel and the Sea Witch Ursula but is unable to do so as Ursula explains it is "...proofed even from [you]" i.e that it is a legal document and the King cannot violate the law.

He is then able to use it to sign his own name on a similar contract to exchange himself in exchange for Ariel's wellbeing. Ownership of the crown and trident seems to convey power over the ocean as Ursula is able to use it to create a whirpool and hurl lightning bolts at Ariel as well as growing to many times her size.

When King Triton is restored he not only uses his Trident to prop himself up on a wave to introduce himself to Eric but uses the Trident's magic to give Ariel a pair of legs (and presumably less family friendly organs too for which no doubt Eric thanks him at a later date.)

Hope this helps!