For the manuscript tradition, see:
http://pinakes.irht.cnrs.fr/notices/oeuvre/18034/
For the edition, see Bibliography.
Discussion
Halkin (1981, 238) suggests the text may date from the 9th century, but in the absence of any specific indications to the contrary, it could also be much earlier.
Bibliography
Text:
Halkin, F. (ed.), "La Passion ancienne de s. Théodote, évêque de Cyrénie en Chypre," Analecta Bollandiana 99 (1981), 239-246. (BHG 2434)