
Fighting Style Feat (Prerequisite: Fighting Style Feature)
When you make an extra attack as a result of using a weapon that has the Light property, you can add your ability modifier to the damage of that attack if you aren’t already adding it to the damage.

Huh?
you add the modifier to the damage, what made you confused?
The "if you aren't already adding it to the damage" part
is to prevent things like "oh this magic dagger that i have lets me add my modifier into the damage even if i use the light property so i guess i add 3 damage + the 3 of my feat so 6 dmg", they made it as a fail safe for min max probably
It means that you don't add the modifier to the damage again if you already have some other feature that lets you do that.
I think anyone with a secondary light weapon can make an extra attack in D&D 2024. Having the Two-Weapon fighting style or feat, I believes then allows you to add ability modifier to damage, and not for anyone else just using a second "light" weapon. I tried to find corroberation of this, but could not find it.
I looked again and found it. It really messes up my dual wielding build, because in order to use two-weapon fighting, both weapons must be light to allow the extra bonus action attack. Frak!