“We have writings from many of them, including Pope St. Clement I, St. Barnabas, St. Polycarp, and St. Ignatius of Antioch.”
From Clemens Romanus, the alleged “Pope” you mention, on Sola Fide, Predestination, and the immutability of God’s will:
“Whosoever will candidly consider each particular, will recognise the greatness of the gifts which were given by him. For from him have sprung the priests and all the Levites who minister at the altar of God. From him also [was descended] our Lord Jesus Christ according to the flesh. Romans 9:5 From him [arose] kings, princes, and rulers of the race of Judah. Nor are his other tribes in small glory, inasmuch as God had promised, Your seed shall be as the stars of heaven. All these, therefore, were highly honoured, and made great, not for their own sake, or for their own works, or for the righteousness which they wrought, but through the operation of His will. And we, too, being called by His will in Christ Jesus, are not justified by ourselves, nor by our own wisdom, or understanding, or godliness, or works which we have wrought in holiness of heart; but by that faith through which, from the beginning, Almighty God has justified all men; to whom be glory for ever and ever. Amen.” (1st Letter to the Corinthians, Chapter 32. We are Justified Not by Our Own Works, But by Faith.)
“Let us consider, then, brethren, of what matter we were made—who and what manner of beings we came into the world, as it were out of a sepulchre, and from utter darkness. He who made us and fashioned us, having prepared His bountiful gifts for us before we were born, introduced us into His world. Since, therefore, we receive all these things from Him, we ought for everything to give Him thanks; to whom be glory for ever and ever. Amen.” (Ibid., Chapter 38. Let the Members of the Church Submit Themselves, and No One Exalt Himself Above Another.)
“By the word of His might He established all things, and by His word He can overthrow them. Who shall say unto Him, What have you done? Or, Who shall resist the power of His strength? When, and as He pleases, He will do all things, and none of the things determined by Him shall pass away.” (Ibid., Chapter 27. In the Hope of the Resurrection, Let Us Cleave to the Omnipotent and Omniscient God.)
Ignatius on predestination and final perseverence:
“Ignatius, who is also called Theophorus, to the Church which is at Ephesus, in Asia, deservedly most happy, being blessed in the greatness and fullness of God the Father, and predestinated before the beginning of time, that it should be always for an enduring and unchangeable glory, being united and elected through the true passion by the will of the Father, and Jesus Christ, our God: Abundant happiness through Jesus Christ, and His undefiled grace.” (Ignatius of Antioch, Epistle to the Ephesians, Ch. 0)
“Seeing, then, all things have an end, these two things are simultaneously set before us— death and life; and every one shall go unto his own place. For as there are two kinds of coins, the one of God, the other of the world, and each of these has its special character stamped upon it, [so is it also here.] The unbelieving are of this world; but the believing have, in love, the character of God the Father by Jesus Christ, by whom, if we are not in readiness to die into His passion, His life is not in us.” (Ignatius of Antioch, Epistle to the Magnesians, Ch. 5)
“Ignatius, who is also called Theophorus, to the Church which has obtained mercy, through the majesty of the Most High Father, and Jesus Christ, His only-begotten Son; the Church which is beloved and enlightened by the will of Him that wills all things” (Ignatius of Antioch, Epistle to the Romans. Ch. 0)
“I give you these instructions, beloved, assured that you also hold the same opinions [as I do]. But I guard you beforehand from those beasts in the shape of men, whom you must not only not receive, but, if it be possible, not even meet with; only you must pray to God for them, if by any means they may be brought to repentance, which, however, will be very difficult. Yet Jesus Christ, who is our true life, has the power of [effecting] this.” (Ignatius of Antioch, Epistle to the Smyrnaeans, Ch. 4)
“Flee, therefore, those evil offshoots [of Satan], which produce death-bearing fruit, whereof if any one tastes, he instantly dies. For these men are not the planting of the Father. For if they were, they would appear as branches of the cross, and their fruit would be incorruptible.” (Ignatius of Antioch, Epistle to the Trallians, Ch. 11)
The real question is, when did the Romish church apostatize from the faith?
No source again......sad.
“From Clemens Romanus, the alleged “Pope” you mention, on Sola Fide, Predestination, and the immutability of God’s will:”
Nowhere in the passage did Clement say we are justified by faith alone.
In fact:
St. Clement of Rome:
“Let us clothe ourselves with concord and humility, ever exercising self-control, standing far off from all whispering and evil-speaking, being justified by our works, and not our words.”
First Epistle of Clement to the Corinthians, Chapter 30.
http://taylormarshall.com/2009/09/did-clement-of-rome-teach-justification.html