What to do when fuel is exhausted and we are denied landing by ATC?
You should have declared an emergency long before your fuel was exhausted. If you haven't yet, do it now.
Land Anyway
You are authorized to do whatever it takes to get the aircraft down, worry about regulations when you are alive enough to do it. Until then, ATC will clear out anything around you, just say &quot;declaring an emergency&quot; and then fly the plane regardless of what ATC &quot;authorizes&quot; you to do or not.
The literal call to ATC will be:

KXYZ, Unable, emergency, landing now.

But only if you have time to make the call.