Data wearing a deerstalker cap; La Forge wearing a bowler hat
An Only wearing a deerstalker cap
A deerstalker cap was a type of 19th century hunter's cap, designed with a brim on the front and back, with flaps that folded down over the ears.
Data wore a deerstalker cap as part of his role as Sherlock Holmes in his Sherlock Holmes Program 3A scenario in 2365. (TNG: "Elementary, Dear Data")
This type of hat was identified in the episode's script.
An Only boy who lived on Miri in 2267 wore a deerstalker cap. (TOS: "Miri")