For the manuscript tradition, see:
http://pinakes.irht.cnrs.fr/notices/oeuvre/14957/
http://pinakes.irht.cnrs.fr/notices/oeuvre/14958/
For the edition, see Bibliography.
Discussion
The Martyrdom of Konon is one of three south Anatolian hagiographic traditions concerning martyrs with this name – the other versions (E06711, E00359) present Konon as a martyr in Isauria (S00430), and as a martyred gardener in Magydos in Pamphylia (S00177). Given their common provenance from the same broad area (the neighbouring provinces of Pamphylia, Isauria and Lycaonia), it is possible that these three traditions represent different versions of the same cult.
Bibliography
Text (BHG 360):
Acta Sanctorum, Maii VII, 5-7 (3rd ed., 6-7).
Caporale, G., Il martirio e culto dei santi Conone e figlio protettori della città di Acerra (Napoli, 1885), vi-ix.