All of the patches, I believe, from the original series were hatched from the fertile mind of Bill Theiss.
patch (to me, at least) seems to be an "art deco-ish" concept of a planet-like heavenly body (not one of the female guest stars that Kirk seduced) traversing the galaxy. The Exeter
Patch seems to be the 'blazed paths' between five heavenly bodies...
By the way, the Enterprise
patch seems to be a stretched, rotated and off-center version of the Federation pennants seen on the sides of the ship. The Defiant
patches seen in "In A Mirror, Darkly" seem to be a different type of off-shoot of the pennant.