I'm confused about how negative effects work on support gems

[Skyward]

Take this support gem for example: Supported attacks gain +25% of damage as extra lightning damage. It also says, supported attacks deal 50% less cold and fire damage. So, if I use this support gem in say Lightning Arrow (which only does lightning damage) then this support gem has no negative effects on any of my other skills that use other types of damage?

[Zenogias]

It depends on any equipment of your as well.

Let'Say if you glove , ring or weapons has any elemental damage mods on it this gem would affect those damages as well.

If you weapons has some kind of mod like Add fire damage,physical damage,cold damage.

This support gems affect all of those mods while you are using the skill that you linked with the support gem.

[postgresql5432]

weapon/gear also have extra elemental damage as well, some keystone or other support
(link on same skill) might got negative effect from this. in future we might have some support skill that will change default element of skill

[Minase]

Yes, you are correct. The support gem only affects the skill gem to which it is equipped. This is what it means when it says "Supported attacks". So any attacks used by that skill gem will deal 50% less cold and fire damage. Note that "attacks" are not spells, or any other type, they are attacks.

[Elon's Musk]

Yeah, use it to bolster the kind of damage you want to focus on - it only impacts the gem it's socketed into. Don't forget you can swap those gems out on the fly too. Really useful for stuff with aoe where you might want scatter shot for mob clear and then swap to concentrated effect that makes the aoe smaller but way more damage for a boss fight.