Yes.
And in this respect I am justly indignant at this so open and manifest folly of Stephen, that he who so boasts of the place of his episcopate, and contends that he holds the succession from Peter, on whom the foundations of the Church were laid, should introduce many other rocks and establish new buildings of many churches; maintaining that there is baptism in them by his authority. For they who are baptized, doubtless, fill up the number of the Church. But he who approves their baptism maintains, of those baptized, that the Church is also with them. Nor does he understand that the truth of the Christian Rock is overshadowed, and in some measure abolished, by him when he thus betrays and deserts unity. The apostle acknowledges that the Jews, although blinded by ignorance, and bound by the grossest wickedness, have yet a zeal for God. Stephen, who announces that he holds by succession the throne of Peter, is stirred with no zeal against heretics, when he concedes to them, not a moderate, but the very greatest power of grace: so far as to say and assert that, by the sacrament of baptism, the filth of the old man is washed away by them, that they pardon the former mortal sins, that they make sons of God by heavenly regeneration, and renew to eternal life by the sanctification of the divine layer. (St. Firmilian, in St. Cyprian, Ep. 74:17)
This was in 256 AD. St. Stephen's letter is otherwise unpreserved - strangely, St. Cyprian makes no mention of this. We may suppose that St. Victor may have made a similiar claim during the Quartodeciman controversy - St. Irenaeus appears to concede his right to excommunicate the Asian churches, and it is hard to imagine from where else it might have derived. But there is such a great lack of writings from this period on ecclesiastical government that it is impossible to bring firm proof otherwise. The other possible reference is this:
After such things as these, moreover, they still dare--a false bishop having been appointed for them by, heretics--to set sail and to bear letters from schismatic and profane persons to the throne of Peter, and to the chief church whence priestly unity takes its source; and not to consider that these were the Romans whose faith was praised in the preaching of the apostle, to whom faithlessness could have no access. But what was the reason of their coming and announcing the making of the pseudo-bishop in opposition to the bishops? (St. Cyprian, Ep. 54:14)
"[W]hence priestly unity takes its source" can quite reasonably be connected to what he says about St. Peter in his treatise "On the Unity of the Church":
Upon one He builds His Church, and though to all His Apostles after His resurrection He gives an equal power and says: 'As My Father hath sent Me, even so send I you: Receive the Holy Ghost, whosesoever sins you shall have remitted they shall be remitted unto them, and whosesoever sins you shall have retained they shall be retained', yet that He might make unity manifest, He disposed the origin of that unity beginning from one.
My other question is about the origin of Petrine Supremacy as a doctrine. This doctrine is credited to Pople Leo I, but that is 400 years after the Church was established. If the Church were established in 1605, we would be just now declaring Papal Supremacy! That's a very long time, you must admit.
Perhaps you can shed some light as to what prompted this doctrine.
As for +Cyprian, he is known to have been the strong advocate of the Pope and a united Church. In his "De Unitate" he writes:
"The other Apostles were indeed what Peter was, endowed with a like fellowship both of honour and of power, but the commencement proceeds from one, that the Church may be shown to be one. This one Church the Holy Ghost in the person of the Lord designates in the Canticle of Canticles, and says, One is My Dove, My perfect one, one is she to her mother, one to her that bare her. He that holds not this unity of the Church, does he believe that he holds the Faith? He who strives against and resists the Church, is he confident that he is in the Church?"
However, in the same work on the Church unity is a marginal addition to this statement, which appears only in this particular copy which, according to the Catholic Encyclopedia, St. Cyrprian "appears most probably to have added," that is it -- it is uncertain.
The marginal text says this:
"And though to all His Apostles He gave an equal power yet did He set up one chair, and disposed the origin and manner of unity by his authority. The other Apostles were indeed what Peter was, but the primacy is given to Peter, and the Church and the chair is shown to be one. And all are pastors, but the flock is shown to be one, which is fed by all the Apostles with one mind and heart. He that holds not this unity of the Church, does he think that he holds the faith? He who deserts the chair of Peter, upon whom the Church is founded, is he confident that he is in the Church?"
This is night and day.
But, if memory serves me right, Cyprian changed his endorsement of papacy and taught of equality among bishops, and that bishops should be "fired" by the laity, all of which got him expelled from the City of Rome where he went to see the Pope. The Pope refused to see him and St. Cyprian was expelled from the city as a heretic.
Moreover, while clearly supporting the idea of Church unity through the throne of Peter, he challenged the Pope over the issue of baptism, rallying 87 African bishops to oppose the Pope! Without going into a debate, it seems clear that the idea of papal power and supremacy was quite different than the idea one gets from Pope Leo I, or from Vatican I.
I think Agrarian observes rightly then that there was no consensus in the early Church (and +Cyprian lived over 200 years after the Church was established) about Pope's infallibility or supremacy.
My last question to you is: where and when and by whom did the title "The Vicar of Christ" originate?