The Mother Church is Jerusalem not Rome Acts 15
In Christianity, a mother church is the church "considered as a mother in its functions of nourishing and protecting the believer"
a mother-church, is sometimes taken for an original church planted immediately by the Apostles, whence others were derived and afterwards spread. And in this sense the Church of Jerusalem is called 'the mother-church of all churches in the world.'"
It was in Jerusalem that the Church was established on the day of Pentecost with the descent of the Holy Spirit on the disciples of Jesus Christ (Acts 2:1-41) and the Gospel of Christ spread from Jerusalem.
Beginning in Jerusalem, the gospel creates ever-widening circles in the world, just as a stone sends out ripples in a pond.
In the first and second century, Christianity consisted of an unknown number of local Churches that in the initial years looked to Jerusalem as its main centre and point of reference
When disproving that Peter is "the first pope" it is customary to turn to Acts 15, where it is stated that James (the Lord's half-brother) was clearly the chief spokesman for the ecclesia at Jerusalem; not Peter. In ch. 8:14 there is equally indisputable proof in regard to the question. Use of the terms "the apostles" and "they" are clear indicators that Peter possessed no supremacy over his fellow apostles. The decision to send Peter and John to Samaria was the result of a consensus discussion among all the apostles. Had Peter held any special authority over his fellows, he would either have elected to travel himself, or would have ruled as to who should be deputed in his place. No such thing occurred. The situation was similar to that recorded in ch. 6:2, "Then the twelve called the multitude of the disciples unto them, and said..." This is now the sixth time that the names of Peter and John are linked together in their work in the Truth. This is the last time that John's name is mentioned in the book of Acts.
Eusebius provides the names of an unbroken succession of thirty-six Bishops of Jerusalem up to the year 324. The first sixteen of these bishops were Jewish—from James the Just to Judas († 135)—and the remainder were Gentiles
Jerusalem was the first center of the church, according to the Book of Acts, and the location of "the first Christian church". The apostles lived and taught there for some time after Pentecost. Jesus' brother James was a leader in the church, and his other kinsman likely held leadership positions in the surrounding area after the destruction of the city
The apostles had a regular meeting place in Jerusalem, an upstairs room where they usually stayed (verse 13: τὸ ὑπερῷον; cf. Acts 9:37,39; 20:8).
The bishop’s seat, the symbol of James’ position as leader, was an object of interest, right up to Eusebius’ day. It is clear that in the first centuries of church history, the Holy See was not in Rome, but in Jerusalem:
Now the throne of James, who was the first to receive from the Saviour and the apostles the the office of a bishop of the church at Jerusalem, who also, as the divine books show, was called a brother of Christ, has been preserved to this day; and by the honour that the brethren in succession there pay to it, they show clearly to all the reverence in which the holy men were and still are held by the men of old time and those of our day, because of the love shown them by God (Eusebius, Ecclesiastical History VII 19