Ask your DM if you can use the "Intimidation" skill
Intimidation is normally used in game for extracting information from enemies, or persuading them to do something for you by force of personality.
It's a skill that Paladins can have proficiency in at character creation, it's charisma-based, and it's meant to strike fear into your foe's hearts — you could ask a DM if they could work out a way for you to use it mechanically to create a "frightened" condition in foes.
Be careful with how you approach this though — "Frightened" is an actual D&D condition with in-game effects (creatures have disadvantage on ability and attack checks when you're in sight of them, and they cannot willingly move closer to you) so being able to cause this condition with an ability check is a significant benefit in itself.
If a DM does implement this, they would most likely set the DC for a successful check based on circumstances, or choose a skill or saving throw for enemies to make against your skill check. They may also impose advantage/disadvantage under certain circumstances.
Also remember that any agreement you come to with a DM will be a house-rule, which won't carry over to any other games you play unless that DM agrees as well (and also won't be usable in any official Adventurers League groups).