Your "Genie" can't be any more powerful than a regular PC
Just to get it out of the way, you'd be building your genie to the same PL limit as anyone else, so your "wishes" need to built just like any power.
But that really doesn't limit them that much
Variable lets you manifest a large number of powers. With Affects Others, you can even give powers to other people (up to what your GM consider appropriate). Transform gives you a lot of options for turning one thing into another. And you just give them whatever other powers make sense from Blast to zap things on command to Flight to get around to Morph to do your best Robin Williams impressions. As for the idea of only being able to do what is commanded, that's more or less a Complication for when it would be convenient to be able to do more, but practically speaking, most of the time such characters just get to do what they will, the same way that you can generally dictate the actions of your minion.
The question is, what do you want do with the character?
I'm not certain whether you're genuinely wanting to always be ordered around, or if it's more flavor. Having a kid sidekick who's the one commanding you still gives you agency, but adds the Complication that you need to keep track of them, and that sometimes the GM may dictate their actions. Or were you looking to gain some sort of additional benefit from only being able to do what is ordered, a point break or an end-run around PL?
Much like utility characters in the game, this might be the sort of concept that shows up in the comics, but which doesn't really work all that well to play.