This website you are copying/pasting from doesn’t look to be completely reliable or hard fact-checked…
It’s mostly speculation. The tradition ever since Papias in the early 2nd century was that Matthew wrote a document, which he calls the
Logia, “in the Hebrew language” (which does not necessarily denote the language we call today Hebrew, but could also mean the tongue in common use amongst many Palestinian Jews at the time: Aramaic), and that “each one interpreted them as best he could.”
It is from Papias’ information that the Fathers derive the idea of Matthew writing the so-called “Gospel of the Hebrews”. He is usually spoken of as being the first to write down a gospel, but this is usually in the context of this ‘Hebrew’ work (Irenaeus,
Against Heresies 3.1.1; Origen,
Commentary on Matthew, as cited in Eusebius,
Ecclesiastical History 6.25.3-6; Eusebius,
Ecclesiastical History 3.24-6-7; St. Ephraem,
Commentary on the Diatessaron; St. Jerome,
Prologue of the Four Gospels &
Letter to Pope Damasus; Pseudo-Athanasius,
Synopsis of Sacred Scripture). Many of them are silent as to exactly how the canonical Matthew (in Greek) came to be, although some hold it as a translation of the Hebrew (Pseudo-Athanasius proposes that James the Just, the ‘brother of the Lord’ and head of the Church in Jerusalem, was the translator).
We have no clear indication from Papias as to when Matthew was supposed to have written these ‘Oracles’ down, although St. Irenaeus holds that it was written when “
Peter and Paul were preaching at Rome, and laying the foundations of the Church.” Other authors add that it was penned in Judaea, more specifically in Jerusalem, for Jewish Christians. If Irenaeus’ information is correct, this would put the writing of Matthew’s ‘Hebrew’
Logia around the mid-to-late 50s up to the 60s (if we follow the traditional reckoning).
I might say that the chronology has a
very early date for the death of James the Just (AD 54). While Nero did become emperor in 54 after the death of Claudius, James’ death, based on what the Jewish historian Josephus says (
Antiquities 20.9), is usually placed somewhere around AD 62, after the death of the procurator Porcius Festus yet before Lucceius Albinus took office. Some scholars would even opine - based on the use of other sources (usually later ones) such as Clement of Alexandria and Hegesippus - that James’ death occurred much later, during the eve of the destruction of Jerusalem (AD 69).