Does a Paladin’s Aura of Courage prevent or suspend frightened effects?

While you’re standing in a Paladin ally’s Aura of Courage:

[the Paladin] and friendly creatures within 10 feet of [the Paladin] can’t be Frightened while [the Paladin is] conscious.

Does this prevent effects that cause Frightened from applying at all, or only suspend them while you stand near your Paladin?

Example: I am standing next to my level 10+ Paladin friend, and we are facing an Ancient Red Dragon. It uses its Frightful Presence.

Do I:

A) Do nothing – I am immune to this effect as a result of the aura.

B) Roll the saving throw – and if I fail the effect is applied to me, but the Frightened condition involved in it is suppressed as long as I am near my Paladin.

This Q&A asks a similar question, but after such an effect has already been applied to a PC – I feel the answer may be different when it comes to the initial application of the effect.

Due to the identical wording, it’s likely that any answers to this question would apply to the Devotion Paladin’s Aura of Devotion and charm effects as well.