I've tried to pin down what they're called, but they're those long white hats that fold at the top and trail down the back. They look cool, but they look completely impractical as a field military uniform. Did they actually wear them out to battle, or were they just for ceremonial use?
If you're interested, those hats were called börk. Here's one from the 17th. c
From what I can tell, the best evidence we could have of whether or not they wore these hats into battle is from miniatures and/or descriptions of the time.
This is a miniature of the time, from an apprentice of the polymath Matrakci Nasuh, which shows Janissaries in the Siege of Rhodes, from which we could come to the conclusion that they did wear them in battle. Given also that these hats represented somewhat of a 'community' between Janissaries, they would most likely have worn them in battle to show that they were the Janissaries.
Source: The Janissaries - David Nicolle, 1995
