If something is countable (e.g. disk space) but is limited by some quota. What you will ask: "how much" or "how many" quota do I have?"
When you can count something, use many:
How many people were at the party?
When you can't count something, use much:
There was too much paint on the walls.
A quota is a limit; it is not countable. What it limits might or might not be countable. So with quota, you should use much:
How much is my quota?
However, it's also very common to say:
What is my quota?