My phone bill shows that I use approx .0005 of data every day at approx 2am. I am not awake or using my phone at this time, plus I am at home and connected to WIFI. Even if there was some app running in the background every night, why would it be using data and not wifi? Does anyone else see this on their bill or know what it is?
Have you tried viewing your data usage on the phone prior to going to sleep; take screen shots and then do the same thing when you wake to see where the little bit of data comes from? Do you keep mobile data turned off while on Wifi?