Wizkids Rules!

Triphasic Emitters states:

Choose a Non Borg weapon Upgrade with a cost of 5 sp or less and place it face down beneath this card.

ATTACK: Discard this card.

Flip the card that is beneath this card face up and perform the attack listed on that card (if possible). After the attack resolves, discard that card.

Can you put Thoron Shock Emitter (or any other class/ship restricted weapon) under Triphasic Emitters?

This is contingent upon what ship the Triphasic Emitters Weapon Upgrade is equipped to.

As long as the card under Triphasic Emitters could normally be equipped to the ship Triphasic Emitters is equipped to, you may placed it beneath Triphasic Emitter.

In your specific example, you would only be able to place Thoron Shock Emitter beneath Triphasic Emitters if Triphasic Emitters was equipped to a Cardassian ATR-4107.