Don Ellis's exercise book "Quarter Tones" he uses arrows to designate the quarter tone notes, although he does not name the notes. These are up arrows and down arrows written like normal accidentals. If you had a sharp note like a C# that you wanted to play a quarter tone low you would have a down arrow and a sharp accidentals preceeding the note.
I have one of Don's horns with the fourth valve extension. It is a flat piece of metal about 1 inch long with a threaded hole at one end for the valve button to screw into, and a hole at the other end for a screw to attach to the valve stem. This way you can play the fourth valve with your pinky without having to reach for it.
The horn is a bit awkward to hold since you have to hold a four valve cluster, rather than three.
In his book Don explained that he first started talking about quarter tone horns in January 1965 with Perry Pirone, a prominent mouthpiece maker and repairman on the east coast. He approached the Frank Holton Company about building one, but got no immediate results, although they were interested in the horn.
In March 1965 Don was told that Pavel Batny, a noted jazz and symphonic composer in Czechoslovakia, was experimenting with quarter tone trumpets. He had composed a piece for a player who had a quarter tone trumpet. Don informed the Frank Holton Company that someone had already build a quarter tone horn and got immediate response. He received his first quarter tone trumpet in September 1965.
If you don't know Don's playing you must get a few CD's and listen. His playing is amazing.