You don't need to eat anything to burn fat while you sleep....Keep in mind, you are in a 8 hour fast each night while you're sleeping.....if you want to burn more fat, one way to do it is by EXTENDING that fast to 14-16 hours by not eating breakfast right away.
This is called intermittent fasting.
I would suggest you try this if you want to burn fat overnight...You could either eat your last meal 6-8 hours before bedtime, or after waking, not eat anything for 6-8 hours.
You COULD have coffee with less than 50 calories worth of milk/sugar, this will not break the fast..
But none of this is going to be of benefit to you if you're not maintaining a caloric deficit. You need to be taking in less calories then your body needs to maintain it's current weight or this will all be for nothing.
You find this out with this formula: (body weight in lbs x 15)
So if you were 150 pounds, that would be 150x15 = 2,250
calories/day...all you'd have to do is couple the fasting with eating less than this amount to maximize the fat burning benefits of fasting.
Once you get a good diet/exercise plan that yields fast results, you won't be sweating gimmic'y stuff like how much fat you're burning overnight.
Here's a good one to start with.