For Polycarp, I’ll let you google Ignatius yourself.
Proportionate to the length of what they wrote, Polycarp has two or three times more quotations and reminiscences from the New Testament that does Ignatius. Of 112 Biblical reminiscences, about 100 are from the New Testament with only a dozen from the Old Testament. Polycarp does not refer to older Christian writings by name, but The Letter to the Philippians has quotations (of approval) from these writings:
Gospel according to Matthew
Gospel according to Mark
Gospel according to Luke
Acts
I Corinthians
II Corinthians
Galatians
Ephesians
Philippians
I Thessalonians
II Thessalonians
I Timothy
II Timothy
Hebrews
I Peter
I John
III John
In fact, The Letter to the Philippians is a mosaic of quotations from both Old Testament and Christian writings. The letter is important for its early testimony to the existence of various other New Testament texts. English translations of the letter are in the books [LHH] and [Richardson] , and online at Noncanonical Homepage and Christian Classics Ethereal Library. The quotations below follow [Richardson]. For a summary of this evidence see the Cross Reference Table.
http://www.ntcanon.org/Polycarp.shtml
Polycarp | Matthew | |
---|---|---|
2:3 |
"Judge not, that you be not judged; forgive and you will be forgiven; be merciful, that you may be shown mercy; the measure you give will be the measure you get" .... |
7:1,2 |
7:2 |
... "to lead us not into temptation"... |
6:13 |
7:2 |
... "The spirit indeed is willing, but the flesh is weak". |
26:14 |
12:3 |
... "for those who persecute and hate you" |
5:44 |
Polycarp | Mark | |
---|---|---|
5:2 |
.... "a servant of all".... |
9:35 |
Polycarp | Luke | |
---|---|---|
2:3 |
.... "blessed are the poor and those persecuted for righteousness' sake, for theirs is the Kingdom of God". |
6:20 |
Polycarp | Acts | |
---|---|---|
1:2 |
... "whom God raised up, having loosed the pangs of Hades". |
2:24 |
2:1 |
.... "judge of the living and the dead",... |
10:42 |
Polycarp | Romans | |
---|---|---|
6:2 |
... "everyone shall stand before the judgment seat of Christ and each of us shall give an account of himself". |
14:10,12 |
Polycarp | I Corinthians | |
---|---|---|
4:3 |
... "the secrets of the heart". |
14:25 |
5:3 |
... "neither fornicators nor the effeminate nor homosexuals will inherit the Kingdom of God", ... |
6:9,10 |
10:1 |
... "steadfast and immovable" ... |
15:58 |
11:3 |
... "do we not know that the saints will judge the world", as Paul teaches? |
6:2 |
Polycarp | II Corinthians | |
---|---|---|
2:2 |
For "he who raised him from the dead will raise us also", ... |
4:14 |
4:1 |
... let us arm ourselves "with the weapons of righteousness", ... |
6:7 |
6:1 |
...but "always taking thought for what is honorable in the sight of God and men" ... |
8:21 |
10:1 |
...in "the gentleness of the Lord preferring one another", and despising no one. |
10:1 |
Polycarp | Galatians | |
---|---|---|
3:3 |
... -- "which is a mother of us all", ... |
4:26 |
5:1 |
... "God is not mocked", ... |
6:7 |
12:3 |
...and in "his Father who raised him from the dead". |
1:1 |
Polycarp | Ephesians | |
---|---|---|
1:3 |
... "you are saved by grace, not because of works", ... |
2:5,8,9 |
3:1 |
... "the word of truth". |
1:13 |
12:1 |
... as it is said in these Scriptures "be angry but sin not" and "let not the sun go down on your anger". |
4:26 |
12:3 |
"Pray for all the saints" . |
6:18 |
Polycarp | Philippians | |
---|---|---|
2:1 |
... "to whom he subjected all things, whether in heaven or on earth", ... |
3:21 |
9:1 |
... "did not run in vain",.. |
2:16 |
12:3 |
... "the enemies of the cross",.. |
3:18 |
Polycarp | I Thessalonians | |
---|---|---|
11:2 |
"Shun evil of every kind" . |
5:22 |
Polycarp | II Thessalonians | |
---|---|---|
11:4 |
... "do not consider such persons as enemies",... |
3:15 |
Polycarp | I Timothy | |
---|---|---|
4:1 |
But "the love of money is the beginning of all evils". |
6:10 |
4:1 |
... "we brought nothing into the world, and we cannot take anything out", ... |
6:7 |
12:3 |
"Pray also for emperors and magistrates and rulers" , ... |
2:1 |
Polycarp | II Timothy | |
---|---|---|
5:2 |
... "we shall also reign with him"... |
2:12 |
9:2 |
For they "loved not this present world", ... |
4:10 |
11:4 |
"May the Lord grant them true repentance" . |
2:25 |
Polycarp | Hebrews | |
---|---|---|
6:3 |
So then let us "serve him with fear and all reverence", ... |
12:28 |
12:2 |
May God and the Father of our Lord Jesus Christ, and "the eternal High Priest" himself, the Son of God Jesus Christ, build you up in faith and truth and in all gentleness ... |
6:20, 7:3 |
Polycarp | I Peter | |
---|---|---|
1:3 |
In him, "though you have not seen him, you believe with inexpressible and exalted joy", -- ... |
1:8,12 |
2:1 |
"Therefore, girding your loins, serve God in fear" ... |
1:13 |
2:1 |
... "believing on him who raised our Lord Jesus Christ from the dead and gave him glory" ... |
1:21 |
2:2 |
... "not returning evil for evil or abuse for abuse", ... |
3:9 |
5:3 |
... "every passion of the flesh wages war against the Spirit", ... |
2:11 |
7:2 |
... "watching unto prayer" ... |
4:7 |
8:1 |
... "who bore our sins in his own body on the tree, who committed no sin, neither was guile found on his lips".... |
2:24 |
10:1 |
... "loving the brotherhood".... |
2:17 |
10:1 |
... "cherishing one another".... |
3:8 |
Polycarp | I John | |
---|---|---|
7:1 |
For "whosoever does not confess that Jesus Christ is come in the flesh is antichrist", and whosoever does not confess the testimony of the cross "is of the devil"; ... |
4:2,3 |
Polycarp | III John | |
---|---|---|
10:1 |
... "fellow companions in the truth"; ... |
1:8 |
What you are citing is, in fact, oral tradition! Polycarp and Irenaeus learned the faith from the Apostle John.
From the Letter of Irenaeus (a student of Polycarp's) to Florinus:
For I have a more vivid recollection of what occurred at that time than of recent events (inasmuch as the experiences of childhood, keeping pace with the growth of the soul, become incorporated with it); so that I can even describe the place where the blessed Polycarp used to sit and discourse his going out, too, and his coming in his general mode of life and personal appearance, together with the discourses which he delivered to the people; also how he would speak of his familiar intercourse with John, and with the rest of those who had seen the Lord; and how he would call their words to remembrance. Whatsoever things he had heard from them respecting the Lord, both with regard to His miracles and His teaching, Polycarp having thus received [information] from the eye-witnesses of the Word of life, would recount them all in harmony with the Scriptures. These things, through, God's mercy which was upon me, I then listened to attentively, and treasured them up not on paper, but in my heart; and I am continually, by God's grace, revolving these things accurately in my mind.
Ref
You just made my point that scripture was transmitted orally, not in writing.