The Byzantine chronicler Johannes Malalas (ed. Dindorf, p. 273) speaks of him as governor of the first province of Palestine (ἡγεμὼν τοῦ πρώτου Παλαιστίνων ἔθνους), in connection with the sojourn of Hadrian in Antioch (114).
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A similar notice may be found in Johannes Antiochenus (In Müller, "Fragmenta Historicorum Græcorum," iv. 580, No. 111) and in Suda, s.v. Τραϊανός.