Updated: May 7, 2020
8. The time of writing is elicited from the narrated traditions of the ancients, especially the Eastern Fathers. How do the Arabs assert that it was written in Palestine and India?
That Matthew wrote the first of all the Gospels, and at Jerusalem, Athanasius in his Synopsi, Chrysostom, and Theophylact relate.Eusebius also, in Historia Ecclesiastica, book III, section 24, narrates that Matthew, proclaiming the faith first to the Hebrew, being about to turn thence unto other nations also, wrote his Gospel in his ancestral language; so that he might supply that which hitherto appeared superfluous with him present, in writing to those whom he was leaving.That this is the sense of the words of Eusebius, against Christophorsonus, who attributed to Eusebius this opinion, that Matthew wrote the Gospel after departing from the Jews, by his own παρερμηνείᾳ/ misinterpretation of the words, the most learned Valesius shows, Annotationibus on that place,page 52.But, that he wrote that Gospel in the first year of the Rule of Claudius, in the ninth year after the ascension of the Lord into Heaven, that most ancient Arabic Codex, illustrated by Kirstenius, pages 24, 25, relates:although Kirstenius in the same place, by comparing the same Codex with Eusabius’ Chronico, strives to prove that, in the third year of the Rule of Gaius Cæsar, or in the eighth after the ascension of Christ into Heaven, that Gospel began to be written, and was at length finished in the next.But also the Arab Translation, and that most ancient Codex of Beza in the subscript, indicate that this Gospel was written in Palestine in the eighth year after the ascension of Christ.Yet Nicephorus, and the Author of the Chronici Alexandrini, have it otherwise, who assert that it was at length written in the fifteenth year after the ascension of Christ into Heaven.Irenæus and Athanasius extend it even further, testifying that Matthew did not begin to write until the two Apostles, Peter and Paul, were already at Rome, and were preaching the Gospel to the Romans; if their testimony is to stand firm, then not a few Pauline Epistles were written before the Gospel of Matthew.But which of these opinions might be better, it is not easy to judge.Nevertheless, those deserve the greatest faith among us, who judge that he wrote first, and that he wrote in Palestine before dispersion of the Apostles, since the consent of many of the ancients drives in this direction, and the Church does not appear to have been long without a written Gospel.I add this one thing, that in the same Arabic Codex of Kirstenius it is found, that that Saint Matthew began to write בפלשטין, in Palæstinis, or in Palestine, a province of Syria, bordering on Arabia; and that he completed it אלהנר, in India, that is Ethiopia.For, learned men observe that sometimes Ethiopians are reckoned by the name of Indians:although with the assertion mentioned above this plainly does not agree, unless it is believed that Jerusalem itself is understood under Palestine.
 John Christopherson (died 1558), a Roman Catholic, served as Master of Trinity College, Cambridge. His translation of Eusebius, Theodoret, Theodore, Sozomen, and Evagrius Scholasticus was published in 1569 under the title Historiæ Ecclesiasticæ Scriptoribus.  Henricus Valesius, or Henri de Valois (1603-1676), was a French Catholic classicist and ecclesiastical historian. He published new editions of Eusebius and other ecclesiastical historians.  Claudius reigned as Roman Emperor from 41 to 54.  Caligula reigned as Roman Emperor from 37 to 41.  Codex Bezæ is a fifth century uncial (covering the Gospels and Acts) of the Western text-type.
Dr. Dilday's Lecture: "Introduction to the Gospels"