Jesus instituted the Petrine Office in the person of Peter (Matthew 16:18) who was succeeded by Linus then Anacletus, etc.
Chain of testimony: St. John the Apostle => St. Polycarp => St. Irenaeus
St. Irenaeus: The blessed Apostles then having founded and built up the Church, committed into the hands of Linus* the office of the espiscopate... To him succeeded Anacletus, and after him, in the third place from the Apostles, Clement was allotted the bishopric... In this order, and by this succession, the ecclesiastical tradition from the Apostles, and the preaching of the truth, have come down to us....
* Make haste to come before winter Eubulus and Pudens, and Linus and Claudia, and all the brethren, salute thee. 2 Tim 4:21
You might want to read post #354 by Elsie. Kinda knocks down the idea you’re suggesting.
>>Jesus instituted the Petrine Office in the person of Peter (Matthew 16:18)<<
Only in Catholic mythology.