Mysterious early morning cellular data usage On my iphone 4s, there are these cellular data usages ranging from 1MB to 80 MB between 1 AM to 3 AM. This happens everyday. anybody knows what's going on and how to avoid it? During that time I am sleeping and the phone is connected to the WiFi.

Secondly I have noticed that when I lock my phone, it starts using cellular data instead of WiFi!!!

I have iOS 8.

Try checking your data usage history, as it seems like a known issue. A lot of people did complain but I can not find a solution to it.
It could be something like this secret (well, not so secret any more) program as detailed in the Wall Street Journal:


  Updated Nov. 13, 2014 8:22 p.m. ET
  
  WASHINGTON—The Justice Department is scooping up data from thousands
  of mobile phones through devices deployed on airplanes that mimic
  cellphone towers, a high-tech hunt for criminal suspects that is
  snagging a large number of innocent Americans, according to people
  familiar with the operations.
  
  The U.S. Marshals Service program, which became fully functional
  around 2007, operates Cessna aircraft from at least five
  metropolitan-area airports, with a flying range covering most of the
  U.S. population, according to people familiar with the program.


I've noticed the same thing myself, and I hear light planes flying over my greater NYC area home in the early morning several times a week. Because I'm a bit paranoid, I turn off my phone at night.