Jobs wouldn't differ that much from those on Earth. Manufacturing would still be common (though arguably mostly automated), and many goods and services will still need to be produced.
The one notable exception I can think of is agriculture. Without land for crops below, working people will have to grow crops up above. Luckily, aeroponics (and hydroponics) are far more efficient than traditional farming, so they make sense given spatial constraints.
Someone needs to harvest and refine all the minerals used to keep people up in the air in the first place. I imagine some surface land will be used as the entrances to deep mineshafts, in which some lower class citizens may work. This could evolve into a feudal system of wealthy landowners leasing land.
If you really want to keep them up in the air, though, asteroid mining is the next best thing. The problem is, the required rockets are too expensive for sky dwellers, unless they're owned and operated by the rich.