In the account of the gospel writers, yes, indeed Peter was the leader of the apostles. However, Jesus was still with them at the time.
In the book of Acts, things have changed. It became “James and the apostles…”; “Tell James and the others…”; Paul “went to see James…”:
I really, really wish you’d give me scripture verses rather than making me research it for you.
I can only presume your first reference, “James and the apostles,” is intended to be 1 Corinthians 15:7. There, it says, about Jesus’ resurrection appearances, “then he appeared to James, then to all the apostles.” That in no way suggests seniority of James- it just says that Jesus appeared first to James and then to all the apostles together. Two distinct appearances that are referred to as two distinct appearances, and who the appearances came to is mentioned. That he made a separate appearance to James before making one to all the apostles doesn’t show anything particular about authority for James either, for this passage says Jesus appeared to Peter before he appeared to the twelve (v. 5).
I can’t find any scriptural reference to, “James and the apostles.” Only this reference to Jesus appearing to Peter, then the twelve, then to the 500, then to James, and then to the apostles. And, “last of all, as to one untimely born, he appeared also to me,” Paul says, very humbly. The special apparition for James came 4th in line

(after the visitation to the 500, too). By mentioning that the appearance to Peter came first, if this passage confers special authority to anyone, it confers it to him. But this passage is only talking about who the apparitions came to and in what order.
Does more research to find the others.
Another passage you referred to is Acts 12:17. This reference, “Tell this to James and the believers,” proves nothing, obviously,
as it is Peter who is speaking! In the lists of the apostles, Peter is always mentioned first and James is one of the first mentioned after him. Therefore if it is Peter that’s speaking, he might particularly single out one of the next greatest in seniority, but it’s obvious he won’t say, “Tell me and the apostles . . .” He’s the one who’s doing the speaking, so he
wouldn’t be included in the list.
I suspect that these two passages I referred to above are the ones you were referring to. The other one, saying Paul went to see James (Acts 21), obviously could not be seen as an indication of authority for James above Peter, as Paul went to see
Peter first thing, before BEGINNING his ministry. If late in his ministry he wants to visit and converse with an apostle, that’s one thing, but to go and talk with Peter first right before beginning his ministry is much more important.
Paul writes in Galations 1:15-19, 'But when God, who had set me apart before I was born and called me through his grace, was pleased to reveal his Son to me, so that I might proclaim him among the Gentiles, I did not confer with any human being, nor did I go up to Jerusalem to those who were already apostles before me, but I went away at once into Arabia, and afterwards I returned to Damascus.
“Then after three years I did go up to Jerusalem to visit Cephas and stayed with him fifteen days; but I did not see any other apostle except James the Lord’s brother.”
Before beginning his ministry, he went away for three years and then went to Jerusalem with the purpose of visiting Cephas. Then he began his ministry.
A meeting much later in the game with James makes absolutely no difference. Apostles can meet with each other if they want. The fact that he went to Cephas before beginning his ministry does suggest Cephas’s leadership and authority, though. In fact, later on in chapter 2, we see Cephas’s authority again. 2:6-9 says that leaders in the churches did not accept Paul’s mission to the Gentiles until “James and Cephas and John, who were acknowledged pillars, recognized the grace that had been given to me.” This also (like the lists of the apostles in the Gospels) suggests that James and John had particular authority in the Church, which might help to explain why Peter sent his letter to “James and the apostles (or ‘James and the believers,’ depending on your translation).”
None of this changes the fact that the Gospel references to Peter and the apostles, and Peter and his companions, confers clear authority to Peter. It’s obvious that a message Peter is sending wouldn’t include himself among those it’s addressed to, though it might single out the next highest in seniority, and it’s obvious that a visit of Paul to James doesn’t prove anything, as it’s late in his ministry and the visit to Jerusalem specifically to meet Peter before beginning his ministry is much more significant, and your reference to James being mentioned 4th in line to see the Christ (followed by a meeting with all the apostles), while the same passage says that Peter saw Him before anyone else in this list, proves nothing except possibly Peter’s particular importance.
These references do not in any way diminish the clear references to Peter’s authority from the Gospels.
In Pauline writings, Paul blamed Peter
Sure, they had one recorded quarrel. Bishops do that sometimes with popes. People often make too big a deal over that one case of clashing wills. Peter, in one of his own epistles, refers to Paul as “our beloved brother.”
James even said “It is my judgment…” to settle a dispute. In the Church History Book II of Eusebius, James was named as the first bishop of the church in Jerusalem.
In other translations, “I have reached the decision . . .” Everyone makes judgments about issues. Acts 15 actually puts more emphasis on Peter, whose words ended the debate. It says there was considerable debate, then Peter spoke, then there was silence, and then Barnabas, Paul and James made concluding and confirming remarks to what Peter had declared. Peter’s words, according to this chapter, ended the debate. "The apostles and the elders met together to consider this matter. After there had been much debate, Peter stood up and said to them . . . (Acts 15:6-7)
Papacy started in Rome, not in Jerusalem.
Because that was the seat of Peter

. The Early Church Fathers repeatedly confirm this. The authority, right from the beginning, was in Rome because that was the Chair of Peter, and his authority was the place “in which sacerdotal unity has its source” (Cyprian of Carthage), the church with which, “all the churches must agree, that is, all the faithful in the whole world,” (Irenaeus), “the church . . . which holds the presidency, in the location of the country of the Romans” (Ignatius [110 AD]). This presidency existed in Rome because that was where the Fathers agreed Peter had led as bishop.
So, after Christ, it wasn’t Papacy yet. Papacy started many years after James and maybe even after the Destruction of Jerusalem in 70 AD.
Papacy, as the scripture references I’ve shown you have shown, started when Jesus said to him, “Your are Peter, and on this rock I will build my Church.” And the Gospels hail him as the leader, and the angel at the resurrection of Jesus called him leader, and he is spokesman for the disciples, held primarily responsible for the faults of the disciples, singled out as first amongst them in every list, and shown clearly as leader when the scripture repeatedly refers to “Peter and the apostles,” or “Peter and his companions.” Jesus also paid taxes for both himself and Peter, but not for the other disciples, because Peter was his special representative, and the man who came to collect taxes from Jesus and his disciples went to Peter, as Peter was Jesus’ representative and spokesman. Note that he didn’t go to Matthew, who was the most skilled at business, taxes and money, nor to Judas, who kept the money bags if I recall correctly. He went to Peter, and Jesus paid for both Himself and Peter.
There are so, so many references to Peter’s special authority, which was universally accepted and hailed among the Early Church Fathers. That was the teaching of Christ Himself, praise be to God. “You will be called Peter, and on this Rock I shall build my Church.”