The Text for this 15-point feat reads as follows

Choose a character.

(optional) Once per turn before this character makes an attack, deal 1 pushing damage to a single target friendly character adjacent to the character; this is not an attack: The character gets +1 to its damage value for that attack. The friendly target does not receive an action token for this pushing damage.

Would I be correct in assuming that said pushing damage would be dealt to said targer friendly character even if they possessed either willpower, power cosmic/quintessence, or indomitable?

Let me know thanks

Here is the current wording :

"DARKNESS WITHIN†
Cost: 15
Choose a character. (Optional) Once per turn before this character makes an attack, deal 1 pushing damage that ignores Willpower and team abilities to a single target friendly character adjacent to the character; this is not an attack: The character gets +1 to its damage value for that attack. The friendly target does not receive an action token for this pushing damage."
(from the unrestricted Player's Guide)

So, characters with Willpower and Power Cosmic/Quintessence team abilities would take 1 pushing damage.
Characters with Indomitable wouldn't, though.

Drunky is correct.