Unfortunately, I don't think what you're looking for exists. As @AlexP says in a comment:
You are chasing a ghost. Epiales is one of the countless "personified abstractions" which populated ancient mythology; he has no other life than his name and function.
I did find some literary references to Epiales, and can confirm that the "source material" for him seems to be more inferred than stated. For example, one "reference" I found mentions Epiales' activities in Oedipus Tyrannus, but the cited reference didn't have Epiales' name - only "the flaming god ... he is a most hateful plague, afflicting the city". Another translation (below) reads "the fiery fever-god... pestilence sweeps the city". Not much to go on, and zero lore.
So, sadly, I don't think there is any lore - or at least none that has survived time! If you're writing a story about Epiales, you can either invent your own, or leave him as a mysterious deity with no formal background or lore. It seems that historically Epiales was simply a personification of natural events.
The most details I could find online came from a book. If you're willing to consider books available online as "(Legit) Online Sources", then after some hunting I came across Disease-spirits and Divine Cures Among the Greeks and Romans by Cesidio Ruel Simboli. Besides a brief mention of Epiales on page 12, he contains the following section on pages 17-18:
THE FEVER GOD EPIALES - This divinity was regarded at once as the sender of fever and the fever itself. He spared neither rich nor poor neither old nor young but attacked whomsoever he could without mercy. The miseries caused by the fever demon says Theognis are worse than the pangs of poverty and the discomforts of exile.
The etymology of the word is doubtful. Some have confused Epiales with Ephiales the giant son of Aloeus. The former was essentially a spirit of sickness. He sent the cold shivering fit preceding fever the fever itself; and terrifying nightmares. Aristophanes and especially the scholiast on line 1098 of the Wasps, speak of Epiales solely in connection with the demon's fever producing activities. Hesychius too refers to him as the sender of chills and fever, and Galen, much later, calls Epiales the quotidian fever.
A vivid description of the terrible work of Epiales is given by Sophocles in the Oedipus Tyrannus. The dramatist is depicting the deadly pestilence which ravaged central Greece. The date of the play is unknown, but Professor Jebb places it between 429 and 420 BC. The fury of the plague, which fell most heavily upon the city of Thebes, was intensified, no doubt, by the unsanitary conditions arising from its surrounding marshes. Complete desolation and despair filled the country, which the god had swept with the might of his unrelenting anger. Oedipus appears ignorant of the great misfortune that had overtaken the city. He inquires of a priest to tell him why he and his followers are so sad and what is the cause of Thebes' ruin. The priest answers:
With your own eyes you see the storm is grown
Too strong, and Thebes can no more lift her head
Out of the waves, clear from the surge of death
A blight is on her budding fruit, a blight
On pasture cattle, and the barren pangs
Of women: and the fiery fever-god
Hath struck his blow - Pestilence sweeps the city,
Empties the house of Cadmus and makes rich
With tears and wailings the black house of Death.
Possibly this passage refers to the great pestilence of 430 BC, whose inroads among the Athenian population were never repaired. It was at this time that the statue of Health - Athena - was set up in the Acropolis as an averter of a possible recurrence of the fatal work of Epiales. Ariphron wrote passionate hymns and chants to the powerful goddess, which sound like fervent prayers for deliverance from the plague. To reinforce the healing activities of Athena, Asklepios, the divine authority in the medical art, was also brought into the city from Epidaurus. The two deities working in cooperation finally succeeded in stopping the plague caused by Epiales and restored health and tranquillity among the devout inhabitants.
The section - which begins here - includes thirteen (13) references (including Theognis, the Iliad, Oedipus Tyrannus, Hesychius). There's also a reference to a book called "Malaria and Greek History", which I could not find a digital copy of, but looks interesting.
Finally, if you're willing to do some offline research, I did find this highly-suspect and not at all trustworthy source: some random tumblr post about Epiales, but at least it has some interesting citations (which I don't care to chase down, but may help you in offline research):
- Atherton, Catherine. Monsters and Monstrosity in Greek and Roman Culture, Levante, 1998.
- Cornford, Francis MacDonald. The Origin of Attic Comedy, Cambridge, 2011.
- Fryer, Evelyn Fern. Greek Literary Mime, Indiana Univ, 1993.
- Harrison, Jane Ellen. Prolegomena to the Study of Greek Religion, Cambridge, 1908.
- Hordern, J.H. ed. Sophron’s Mimes: Text, Translation, and Commentary, Oxford, 2004.
- Jones, William Henry Samuel and Edward Theodore Withington. Malaria and Greek History, Manchester, 1909.
- MacDonald, John M.S. Character Portraiture in Epicharmus, Sophron, and Plato, Univ. Press, 1931.
- Roscher, Wilhelm Heinrich, and James Hillman. Pan and the Nightmare, Spring, 2000.
- Rose, H.J. A Handbook of Greek Mythology. Routledge, 2004.
- Simboli, Cesidio Ruel. Disease-spirits and Divine Cures Among the Greeks and Romans, Columbia, 1921.
- Sommerstein, Alan H. Talking about Laughter: and Other Studies in Greek Comedy, Oxford, 2009.