Damage modifiers for damage you do not have

Playing Arcanist.
Default weapon attack is Panetti’s Replicating Missile (damage type: Elemental).
Main attacks are:

  • Albrecht’s Aether Ray (damage type: Fire & Aether)
  • Trozan’s Sky Shard (damage type: Cold & Lightning)
  • Devastation (damage type: Fire & Aether)
    How does damage modifiers work for damage that I do not have?
    Do they add “0” damage?
    Or, do they add their type of damage to the damage the current attacks do?
    For example:
    Found a Ring of the Black Matriarch which adds +63% Physical, +65% Acid, +72% Internal Trauma & +55% Poisson.
    None of the attacks I use have any of these damage types.
    Does this mean that equipping this ring will yield 0% increase in damage (when I equip the ring the damage done by the above attacks does not change when I hover the mouse over the attack)?
    Or, is there an effect in attack damage (but not shown when hovering the mouse)?

Yes, equipping this ring will give you zero damage increase.

The only case where you get the damage is when for example a ring has flat +10 Acid Damage and you use a skill that has %Weapon Damage. Then this skill gets a percentage of that flat +10 Acid Damage.
Not that it matters when you have very low total %Acid Damage multiplier.