According to the early church historian Eusebius of Caesarea, Quadratus was a disciple of the Apostles (auditor apostolorum), as noted in Chronicon.

Later, after settling in Athens, Quadratus, much like other Athenian apologists such as Aristides and Athenagoras, did not hold a formal position within the Church hierarchy.

The surviving fragment of the discourse shares Quadratus's reflections on the enduring impact of Jesus's miracles, asserting their authenticity and lasting significance.

Holmes noted that, although the Epistle to Diognetus does not contain the sole known quotation from Quadratus' address, there exists a gap between chapters 7.6 and 7.7 where it could potentially fit.

[14] Efforts to associate Quadratus' Apology with the Letter to Diognetus, martyr accounts, or the Barlaam and Josaphat legend have similarly failed to yield convincing evidence.

While The Oxford Dictionary of the Christian Church suggests the possibility of this link, Jerome erroneously conflated the Apologist with the Bishop who served during Marcus Aurelius' reign (161–180).

"[10][15] Quadratus' language suggests that Christ's time on earth was a temporary sojourn, indicating his divine pre-existence before incarnation.

He emphasized the lasting testimony of individuals healed or raised from the dead by Jesus, framing these miracles as genuine and enduring evidence of Christ's divine power.

Quadratus applied the title "Soter" to Jesus, a term with divine connotations in both Jewish and Hellenistic traditions, suggesting Christ's superiority to pagan deities.

Eusebius praised Quadratus' orthodoxy, aligning his Christological views with apostolic teachings, including the deity and miraculous works of Jesus.