I can't find any information about them, what were they called and what was their usage.
Below its a link to a photo with them.
https://upload.wikimedia.org/wikipedia/commons/6/63/Countermand_concession.jpg
Best as I can tell, those are just a conical hat of some sort. It looks like a pretty simplistic variant and likely one that certain soldiers acquired via looting from local populations hence why only a few have them and not the entire marching column. More information about KMT equipment and uniform can be found here https://www.militarytrader.com/.amp/militaria-collectibles/the-military-conical-hat