The kineticist gets an elemental attack which gains damage as the kineticist levels. The kineticist can learn wild talents; some of these are permanent reusable abilities, and others upgrade the elemental attack.
It sounds like you're looking for the 3.5e warlock class, found in Complete Arcane. The warlock gets an eldritch blast which gains power as the warlock levels. The warlock learns invocations; some of these are permanent reusable abilities, and others upgrade the eldritch blast.
If you had your heart set on being specifically an elemental-themed character, your best shot is to ask your DM to let you re-theme your powers, perhaps arguing that you have an elemental prince as your warlock patron.
If your DM doesn't buy that, there's technically a feat that would let you re-theme your powers (Spell Thematics), but it's not in the same book as Complete Arcane, and also the prerequisites are a bit tricky to meet.