You might think that a regular efreeti is a pretty mythic fellow, but once you read through these notes it becomes clear that a true mythic efreeti is even more potent.
Sharing common characteristics with their regular brethren, mythic efreet have additional powers most notable of which is the ability to magically shackle a humanoid creature, enslaving them. A full stat block and notes on their special abilities are provided along with comprehensive notes about how mythic efreet fit into the hierarchy on the Plane of Fire.
This explains how mythic efreet gain 'mythic' status... by interacting with us 'lesser' creatures on the Material Plane! An efreeti who grants too many wishes and warps the fabric of the multiverse enough begins to gain mythic powers.
The rest of the work contains several rituals for summoning mythic efreet. The usual planar binding spells don't work on mythic genies, so other means must be employed. In some ways these rituals are easier than regular summonings, but they are also more risky and the unwary may find themselves unprotected when the summoned efreeti - likely to be in a bad mood - pops out in front of them!
Some interesting twists to throw into run-of-the-mill genie interactions here.