Oath of Conquest paladins emanate an Aura of Conquest starting at 7th level (XGtE, p. 38):
Starting at 7th level, you constantly emanate an aura while you're not incapacitated. The aura extends 10 feet from you in every direction, but not through total cover.
If a creature is frightened of you, its speed is reduced to 0 while in the aura, and that creature takes psychic damage equal to half your paladin level if it starts its turn there.
Conquest Paladins can also prepare the fear spell starting at level 9, which states:
Each creature [...] must succeed on a Wisdom save or [...] become frightened for the duration.
An affected creature must take the Dash action and move away from you by the safest route on each of its turns [...] If the creature ends its turn in a location where it doesn't have line of sight on you, it can make a Wisdom save.
This question makes it clear that the caster is the source of the fear by virtue of being the character to cast it. However, while the caster is the "source" of the fear, it's not clear that this is qualifies as "of you" and fear does not explicitly state that the creatures are afraid of you.
Contrast this with the cause fear spell (XGtE, p. 151), which does state this:
The target must succeed on a Wisdom saving throw or become frightened of you until the spell ends.
Or of the Conquest paladin's Conquering Presence Channel Divinity option, which does as well:
As an action, you force each creature of your choice [...] to make a Wisdom saving throw. On a failed save, a creature becomes frightened of you for 1 minute.
It's clear that a Paladin who uses either Conquering Presence or cause fear would trigger the psychic damage of Aura of Conquest, but would s/he trigger it by casting fear?