%increased damage

The new rare jewels says "10% increased damage"

Redbeak sword says 100% increase damage

The broken crown says 20% increased damage

Bated Breath says 10% increased damage

All these things works well with spell, attack, x-x damage from items

How this will work with minions? or Aura applied to minions etc..?

Bonuses never apply to minions unless they specify minion or are stats that specifically are added to minions.

The second case is pretty much the rule for Support Gems and is what allows things like Multistrike to affect minions.

Outside of Support gems you can only only only only boost minion damage with things that specifically say "minion" in them.

The reason is that minions are not you and do not have your stats. x% increased damage is a stat you have. It's not any more inheritable than other bonuses.