Notice that he is drawing information from Hegesippus in the previous line:
No iron implement had touched his head, he had never visited a bath house, had never eaten meat.41 He did not own a change of clothing and wore only a threadbare linen garment, as it says in the Gospel, "The young man fled, and left the cloth where with he was clad."
The original reference in Hegesippus as cited by Eusebius:
Yes there is a reference to the ending of the Gospel according to the Hebrews but surely there is more than just this:James, the brother of the Lord, succeeded to the government of the Church in conjunction with the apostles. He has been called the Just by all from the time of our Saviour to the present day; for there were many that bore the name of James. He was holy from his mother's womb; and he drank no wine nor strong drink, nor did he eat flesh. No razor came upon his head; he did not anoint himself with oil, and he did not use the bath. He alone was permitted to enter into the holy place; for he wore not woolen but linen garments. And he was in the habit of entering alone into the temple, and was frequently found upon his knees begging forgiveness for the people, so that his knees became hard like those of a camel, in consequence of his constantly bending them in his worship of God, and asking forgiveness for the people.
I infer from this that THE linen cloth is the linen cloth worn by the naked youth in the gospel and that Hegesippus is using the Gospel According to the Hebrews.Also the gospel called according to the Hebrews, recently translated by me into Greek and Latin, which Origen often uses, says, after the resurrection of the Savior: "Now the Lord, when he had given the linen cloth to the servant of the priest, went to James and appeared to him (for James had sworn that he would not eat bread from that hour in which he had drunk the Lord's cup until he should see him risen from among them that sleep)." And a little further on the Lord says, "Bring a table and bread." And immediately it is added, "He took bread and blessed and broke and gave it to James the Just and said to him, "My brother, eat your bread, for the Son of man is risen from among them that sleep.'"[cf. Luke 24:50-53 Gospel according to the Hebrews (in Jerome, On Illustrious Men, 2)]