As for the Bishop of Rome holding a “Primacy” in the early Church, there is plenty of evidence. Now, you say the 1st 50 years after Christ which would put us around 80-85AD.
If we assume the above dating is correct, this would mean that Saint John the Apostle was still alive. So while I can’t provide anything definitive from the Church Fathers as the fist group of them are called the Apostolic Church Fathers because of their connection to the Apostles. One such is St. Clement of Rome who wrote an authoritative Letter to the Church at Corinth. I have provided a link below which is from Calvin College [Reformed University] and has the German Reformed Church History Scholar Phillip Schaff’s translation of Saint Clement of Rome’s Letter [which you can read yourself]. What I have linked is Professor P. Schaff’s introductory Note on St. CLements Letter
http://www.ccel.org/ccel/schaff/anf01.ii.i.html
Now of interest here is that the testimony of later 2nd Century Church Fathers indicates that Saint Clement new the Apostles [Philip Schaff’s introductory note comes to that conclusion, for the record] as Saint Ireneaus of Lyons states that St. Clement “had seen the blessed Apostles” ....had been conversant with them....and might be said to have their preaching echoing in his ears and their traditions before his eyes...
Now we are at the end of the 1st century and what has to be asked here is What does Saint Clement’s intervention into the internal affairs of a Church in the East, i.e. Corinth mean. If we assume an eccelisiology of modern independent Protestantism, then it makes no sense. Corinth would tell Saint Clement to “go take a hike” However, we don’t see that. However, given that Clements letter was recieved by the Church of Corinth, implies that the Church of Rome had a role in calling back the Church at Corinth into orthodoxy. Thus, it is entirely an historical record that the Church of Rome was exercising some “Primacy” at the end of the 1st century.
In addition, in St. Clement’s Letter you will find a 1) clear distinction between the role of the clergy and layman, not that they are in opposition, but all serve in different capacities in the Church, the Body of Christ, 2) and Outline of Apostolic Succession, and 3) Strong Eucharistic Doctrine as he writes “Our sin would not be small if we eject from the episcopate those who blamelessly and holily have offered its sacrafices.
Clement’s letter is usually dated around 95-97AD. Some 10 years after, we get St. Ignatius of Antioch’s Letters [7 authentic] which show strong ecclessiology like the Catholic Church, strong Eucharistic Doctrine and of course the line “The Church of Rome...presides in Love [some translations state Holds the Presidency in Love”. Again, I have linked Schaff’s Introductory note, of course he does downplay that statement while acknowleding that the Church of Antioch and Rome had “Fraternal Relations”, which is a way of avoiding using the word “Communion”. Scaff’s note is honest enough to point out that many in the Protestant world questioned all of the Ignatian corpus because it so clearly laid out a model that is what the Catholic Church looks like and is, and thus many questioned all of it, although he concedes that 7 Letters of Ignatius are now all recognized as authentic by scholars.
So within 75 years of Christ death perhaps within Saint John the Apostles Lifetime [given Clements Letter] there are 2 clear references to the Church of Rome holding some form of “Primacy in the early Church.” On that point, anyone here on FR who doubts that now who has read this thread is being intellectually dishonest. If one wants to question whether Vatican I in its definition of Papal Infallability defined it in a way that was not necessary or was too much of a reach by Rome, then that is a legitimate point to make and discuss, not that I agree with it, but I can understand the argument, particulary from the Eastern Orthodox point of view. But to debate that the Church of Rome had a Primacy is putting your head in the sand and not being honest [which many FR Protestants, not going to name them, do all the time].
http://www.ccel.org/ccel/schaff/anf01.v.i.html
The church of Rome wasn't yielded to on a regular basism in later centuries. The history is spotty. Other bishops had their days or moments of great influence, too.