Conon (mythographer) in Wikipedia
Conon was a Greek grammarian of the age of Augustus, the author of a work entitled Διηγήσεις (Narrations), addressed to Archelaus Philopator, king of Cappadocia. It was a collection of fifty narratives relating to the mythical and heroic period, and especially the foundation of colonies.
An epitome of the work was preserved in the Bibliotheca of Photius the 9th century patriarch of Constantinople. Photius commends Conon's Attic style, and remarks that Nicolaus Damascenus borrowed much from him. There are separate editions of this abstract by Gale; by Teucher;; and Kanne.
Dion Chrysostom mentions a rhetorician of this name, who may possibly be identical.