Flat cap
A flat cap was a type of rounded cap with a stiff brim worn on Earth from the early 20th century through the end of the 24th century. (Star Trek IV: The Voyage Home; PIC: "Remembrance") A newsboy cap was a type of flat cap that was fuller, with a button on top, often worn by news vendors, as the name implies. (TNG: "The Big Goodbye"; DS9: "Far Beyond the Stars")
These types of caps were also worn by Davod, a Zeon on Ekos, and a tough kid Iotian, on Sigma Iotia II, both during the 2260s. (TOS: "Patterns of Force", "A Piece of the Action")
A news vendor wearing a newsboy cap in the 1940s
A newsboy cap worn in the 1950s
A man wearing a newsboy cap in the 1980s
An Iotian boy wearing a newsboy cap in the 2260s
Davod wearing a flat cap in the 2260s
Jean-Luc Picard wearing a flat cap in the 2390s