All References to Peter in Clement of Alexandria in the Instructor

Do you see a pattern here that 'Peter' might have been used to instruct those who had yet to receive the baptism in the Alexandrian Church? It's a distinct possibility, I think, and might support my interpretation of 'the Gospel of Peter' in To Theodore:

Paedagogue 1:6 Wherefore also Peter says: "Laying therefore aside all malice, and all guile, and hypocrisy, and envy, and evil speaking, as new-born babes, desire the milk of the word, that ye may grow by it to salvation; if ye have tasted that the Lord is Christ."

ibid 2.1 That fish then which, at the command of the Lord, Peter caught, points to digestible and God-given and moderate food. And by those who rise from the water to the bait of righteousness, He admonishes us to take away luxury and avarice, as the coin from the fish; in order that He might displace vainglory; and by giving the stater to the tax-gatherers, and "rendering to Caesar the things which are Caesar's," might preserve "to God the things which are God's."

ibid 2.13 Most admirably, therefore, the blessed Peter says, "In like manner also, that women adorn themselves not with braids, or gold, or costly array, but (which becometh women professing godliness) with good works." For it is with reason that he bids decking of themselves to be kept far from them. For, granting that they are beautiful, nature suffices.

ibid 3.10 "And Abraham," it is said, "served up for three, dinner under a tree, and waited on them as they ate." The same with fishing, as in the case of Peter, if we have leisure from necessary instructions in the Word. But that is the better enjoyment which the Lord assigned to the disciple, when He taught him to "catch men" as fishes in the water.

ibid 3.11 For as it is enjoined on them, "to be subject to their masters with all fear, not only to the good and gentle, but also to the froward," as Peter says; so fairness, and forbearance, and kindness, are what well becomes the masters. For he says: "Finally, be ye all of one mind, having compassion one of another; love as brethren, be pitiful, be humble," and so forth, "that ye may inherit a blessing," excellent and desirable.

ibid 3.13 Such injunctions of righteousness uttered by those who are conversant with worldly wisdom are not to be refused. Knowing, then, the duty of each, "pass the time of your sojourning here in fear: forasmuch as ye know that ye were not deemed with corruptible things, such as silver or gold, from your vain conversation received by tradition from your fathers; but with the precious blood of Christ, as of a lamb without blemish and without spot." "For," says Peter, "the time past of our life may suffice us to have wrought the will of the Gentiles, when we walked in lasciviousness, lusts, excess of wine, revellings, banquetings, and abominable idolatries." We have as a limit the cross of the Lord, by which we are fenced and hedged about from our former sins. Therefore, being regenerated, let us fix ourselves to it in truth, and return to sobriety, and sanctify ourselves; "for the eyes of the LORD are on the righteous, and His ears are open to their prayer; but the face of the LORD is against them that do evil." And who is he that will harm us, if we be followers of that which is good?" "us" for "you." But the best training is good order, which is perfect decorum, and stable and orderly power, which in action maintains consistence in what it does.