Are you familiar with the pseudo-Clementine literature, spurious documents written before Stephen, that refer to Peter as having transferred his authority to Clement in Rome, keys, binding and loosing, teaching chair? This document appears to have had wide influence and was thot to be genuine until the Renaissance. Here are some excerpts:
"I lay hands upon this Clement as your bishop; and to him I entrust my chair of discourse, even to him who has journeyed with me from the beginning to the end, and thus has heard all my homilies…Wherefore I communicate to him the power of binding and loosing, so that with respect to everything which he shall ordain in the earth, it shall be decreed in the heavens. For he shall bind what ought to be bound, and loose what ought to be loosed, as knowing the role of the Church. Therefore hear him, as knowing that he who grieves the president of the truth, sins against Christ, and offends the Father of all. Wherefore he shall not live; and therefore it becomes him who presides to hold the place of a physician, and not to cherish the rage of an irrational beast.”
“Therefore take the oversight gladly; and all the more in good time, because you have learned from me the administration of the Church, for the safety of the brethren who have taken refuge with us.”
“…that you may have the care of the Church always, in order both to your administering it well, and to your holding forth the words of truth.”
“…and so let them listen to you, knowing that whatever the ambassador of the truth shall bind upon earth is bound also in heaven, and what he shall loose is loosed. But you shall bind what ought to be bound, and loose what ought to be loosed. And these, and such like, are the things that relate to you as president.”
"Having thus spoken, he laid his hands upon me in the presence of all, and compelled me to sit in his own chair. And when I was seated, he immediately said to me: “I entreat you, in the presence of all the brethren here, that whensoever I depart from this life, as depart I must, you send to James the brother of the Lord a brief account of your reasonings from your boyhood, and how from the beginning until now you have journeyed with me, hearing the discourses preached by me in every city, and seeing my deeds. …when he learns, that not an unlearned man, or one ignorant of life-giving words, or not knowing the rule of the Church, shall be entrusted with the chair of the teacher after me. For the discourse of a deceiver destroys the souls of the multitudes who hear.”