This is based off the show A Certain Magical Index.

As an esper, you were born with powers resembling psionics, but still quite different. You have no apparent reason for your powers, but they are strong, and let you do things that are unusual compared to the average person. These powers can also be honed further, to scopes of high mental prowess.

ESP

Beginning at 1st level, you have found that you draw your powers from something called "ESP". With this, you can pick a signature ability, that will forever be bound to you, and identifies you as an esper. Pick one first level spell you know. You can cast that spell without using a spell slot, at 1st level, once per long rest.

You can cast this as much as you want as a 1st level spell once you reach 10th level, and you can cast it at 2nd level without using a spell slot, once per long rest, once you get to 15th level.

Esper Points

Starting at 2nd level, you will not gain sorcery points, but esper points. These act much like sorcery points, but can't make or destroy spell slots. Rather, you can spend 2 to cast your signature esper spell at 2nd level, and 2 additional points per each level above that.

Amplified Ability

At 6th level, you can cast your signature esper spell at 1st level (or spend points or a spell slot to raise its level), and you can use a meta magic on it. This meta magic will not take any esper points to use, and you can do this a number of times equal to your constitution modifier (minimum of 1) per long rest.

Mental Fortitude

Beginning at 14th level, you have trained your mind well. With mental prowess being one of your key features, the mind must be honed. You now have resistance to psychic damage, and your mind cannot be read, unless you allow it.

Esper Overflow

At 18th level, you have gained such a large amount of esper power, that you now have a surplus. As an action, you can release some of this energy, discharging it within a 20 feet radius. All creature within range must make an intelligence saving throw against your spell save DC. On a failure, they are thrown 10 feet away from you, and take 6d20 psychic damage. They take half as much damage, and aren't pushed back on a success.