First, checking the writings at eCatholic Apostolic Fathers, Justin Martyr, Irenaeus, the only reference to "gates of hell" was "Hell's gates" in St. Iraneaus' (technically, not an Apostolic Father, but whom had seen and heard the Apostolic Father, St. Polycarp) Against Heresies, Book IV, Chapter 33:
Whosoever confesses that one God is the author of both Testaments, and diligently reads the Scriptures in company with the presbyters of the Church, is a true spiritual disciple; and he will rightly understand and interpret all that the prophets have declared respecting Christ and the liberty of the New Testament
- A spiritual disciple of this sort truly receiving the Spirit of God, who was from the beginning, in all the dispensations of God, present with mankind, and announced things future, revealed things present, and narrated things past—[such a man] does indeed “judge all men, but is himself judged by no man.” For he judges the Gentiles, “who serve the creature more than the Creator,” and with a reprobate mind spend all their labour on vanity. And he also judges the Jews, who do not accept of the word of liberty, nor are willing to go forth free, although they have a Deliverer present [with them]; but they pretend, at a time unsuitable [for such conduct], to serve, [with observances] beyond [those required by] the law, God who stands in need of nothing, and do not recognise the advent of Christ, which He accomplished for the salvation of men, nor are willing to understand that all the prophets announced His two advents: the one, indeed, in which He became a man subject to stripes, and knowing what it is to bear infirmity, and sat upon the foal of an ass, and was a stone rejected by the builders, and was led as a sheep to the slaughter, and by the stretching forth of His hands destroyed Amalek; while He gathered from the ends of the earth into His Father’s fold the children who were scattered abroad, and remembered His own dead ones who had formerly fallen asleep, and came down to them that He might deliver them: but the second in which He will come on the clouds, bringing on the day which burns as a furnace, and smiting the earth with the word of His mouth, and slaying the impious with the breath of His lips, and having a fan in His hands, and cleansing His floor, and gathering the wheat indeed into His barn, but burning the chaff with unquenchable fire.
- Moreover, he shall also examine the doctrine of Marcion, [inquiring] how he holds that there are two gods, separated from each other by an infinite distance. Or how can he be good who draws away men that do not belong to him from him who made them, and calls them into his own kingdom? And why is his goodness, which does not save all [thus], defective? Also, why does he, indeed, seem to be good as respects men, but most unjust with regard to him who made men, inasmuch as he deprives him of his possessions? Moreover, how could the Lord, with any justice, if He belonged to another father, have acknowledged the bread to be His body, while He took it from that creation to which we belong, and affirmed the mixed cup to be His blood? And why did He acknowledge Himself to be the Son of man, if He had not gone through that birth which belongs to a human being? How, too, could He forgive us those sins for which we are answerable to our Maker and God? And how, again, supposing that He was not flesh, but was a man merely in appearance, could He have been crucified, and could blood and water have issued from His pierced side? What body, moreover, was it that those who buried Him consigned to the tomb? And what was that which rose again from the dead?
- [This spiritual man] shall also judge all the followers of Valentinus, because they do indeed confess with the tongue one God the Father, and that all things derive their existence from Him, but do at the same time maintain that He who formed all things is the fruit of an apostasy or defect. [He shall judge them, too, because] they do in like manner confess with the tongue one Lord Jesus Christ, the Son of God, but assign in their [system of] doctrine a production of his own to the Only-begotten, one of his own also to the Word, another to Christ, and yet another to the Saviour; so that, according to them, all these beings are indeed said [in Scripture to be], as it were, one; [while they maintain], notwithstanding, that each one of them should be understood [to exist] separately [from the rest], and to have [had] his own special origin, according to his peculiar conjunction. [It appears], then that their tongues alone, forsooth, have conceded the unity [of God], while their [real] opinion and their understanding (by their habit of investigating profundities) have fallen away from [this doctrine of] unity, and taken up the notion of manifold deities,-[this, I say, must appear] when they shall be examined by Christ as to the points [of doctrine] which they have invented. Him, too, they affirm to have been born at a later period than the Pleroma of the AEons, and that His production took place after [the occurrence of] a degeneracy or apostasy; and they maintain that, on account of the passion which was experienced by Sophia, they themselves were brought to the birth. But their own special prophet Homer, listening to whom they have invented such doctrines, shall himself reprove them, when he expresses himself as follows:---
“Hateful to me that man as Hades’ gates,
Who one thing thinks, while he another states.”
[This spiritual man] shall also judge the vain speeches of the perverse Gnostics, by showing that they are the disciples of Simon Magus.
Then, searching for available writings of the rest of the Apostolic Fathers not given on the above eCatholic site:
The Shepherd of Hermas
An aside: Consider the whole quote given above: "Hateful to me that man as Hades’ gates, who one thing thinks, while he another states." Perhaps, it was from this writing of St. Irenaeus (who was from Lyon---not far from Ars, France) that St. John Vianney (patron Saint of all priests) said in a sermon he once gave on lying: ``Nothing is more unworthy of a Christian, whose life should be an imitation of a God Who is the soul of Honor and Truth itself, than to think one thing and say another.'' (cf. Thoughts of the Curé of Ars, TAN Books, 1984, p. 43.)