What do you think of this on the "One Holy Catholic and Apostolic Church?"?

Great question. You know a few of the people you mention here bear a little fleshing out for people who have not been raised with a proper Catholic upbringing. You mention Ignatius. This is not just some yahoo carping about Jesus Christ and Christianity, he was a founding father of the Church. The Roman Catholic Church. Anyone who doubts his veracity is inventing reality. It has been known for almost two thousand years that Ignatius made eloquent for the Church its fundamental thoughts on Eucharist as Christ gave that gift to his Apostles. This is a man who was an eyewitness to Jesus Christ and the miracles of Christ and the Apostles. He is mentioned in the Bible, but more important than that, he directly interacted with the people in the Bible and documented that interaction and those documents survived the catacombs of Rome, where he was killed because of his faith. He is one of the best examples of how centered the Church was in Rome. Of how unified it was even in the face of heretics who tried to say Christ was only a man and not God And Man. And most importantly, he destroyed the arguments of heretics who say the Eucharist is not the body and blood of our Savior Jesus Christ. Now as an aside, it is legend, not tradition now, but legend, that Ignatius is the child referred to in Mark 9:35, when Christ brought a child into the midst of the Apostles and tried to explain how the Kingdom of Heaven would be. St. Peter himself ordained Ignatius who was a most ardent Bishop of the Roman Catholic Church.

You mention Clement, another founding father of Catholicism (unity in Christianity). Clement also knew Peter. His eyewitness accounts of the early Roman Catholic Church are known with certainty because his original documents still exist. Others are reputed to exist, but one epsitle for certain exists. This is yet another extra-Biblical testimony to the great work done in the name of Jesus Christ to continue the Lord's ministry on earth as it was intended: through the Roman Catholic Church, the one started when Christ ordered Peter to "feed my sheep." Feed the Word. Feed Eucharist. Feed faith. Clement was the fourth pope, he personally knew several of the original Apostles of Jesus Christ, and he too was murdered for his faith by the Romans. But again, his writings survived the catacombs of Rome. They were not included in the Bible, but they may well could have been. Certainly, they have more veracity than the sketchy garbage attributed to St. Thomas, which a small number of Christians believe is an accurate Gospel. The Church decided not to include it because for many reasons, but if it HAD been included in the Bible, Clement's epistles would easily have "made the cut."

The ancient historian Tertullian placed Clement as the second pope just after Peter, but more than two other sources closer to the actual event place Linus second and Clement fourth (Cletus was the third pope). There is no question that these men were "popes." The historical record is clear. There is zero question that the Church was the one based in Rome. Even St. Paul clarified in his epistles that the Church is One (Catholic, a word that came into popular use later as the language changed). So there is your absolute proof of the Roman Catholic Church being the original church that Jesus Christ started. There is no rebuttal to that argument. If the Bible's record isn't good enough for you, here is what Ignatius wrote on the matter, and he was there, you weren't:

"""After the Holy Apostles (Peter and Paul) had founded and set the Church in order (in Rome) they gave over the exercise of the episcopal office to Linus. The same Linus is mentioned by St. Paul in his Epistle to Timothy. His successor was Anacletus."""

Linus was buried next to St. Peter, a site upon which a thousand-plus years later the Vatican would be built once the Church gained sufficient autonomy and popular consent to build the awesome monument to Christianity. The Vatican is the home to all Christian faithful. It has withstood the hatred of many, not the least of which was Adolph Hitler himself and the entire Nazi and Italian fascist faithful, who murdered some 7,000 priests and Catholic ministers in the concentration camps of Eastern Europe. Out of those ashes came Pope John Paul II from Poland and Pope Benedict XVI from southern Germany. Both miraculously survived and today take their place in the line of Apostolic Power that Ignatius, Linus, Cletus and Clement solidified in the first century of the Church. Pope John Paul II during his years as Servant to Us All could step down to the Vatican archives not only to pray beside the bones of these Church treasures, but also to lay his hands on the actual documents they drafted as well as studies of the documents done by St. Jerome, Augustine, Aquinas and countless others that have made Catholicism the truth, the way and the light towards faith and Christlike behavior.

Also mentioned in this question is St. Cyprian. He was a convert to Catholicism and he followed Christ's example to a T. Perhaps his example can inspire those who hate Catholics and who espouse all sorts of nonsense about the Roman Catholic Church. A link is included below to read about St. Cyprian from the Catholic Encyclopedia, written 100 or so years ago. Perhaps Cyprian will challenge to conversion those who huddle together with smug bigotry, stubbornly separating themselves from their brothers and sisters in Christ who need them as the Vatican wages vigilant battle against on poverty, ignorance and above all, non-belief. The war already is won; all that matters is how we get from here to there. "Love one another as I have loved you," said Jesus Christ.

Our minds are clear, the reason of the dead of Peter in Rome, was due to preaching the gospel, my question goes to opposer, if he did not start a Roman Catholic church, which did he started?

Thank the Lord for the gift of his Church.

The Catholic church is the true faith founded by Christ Himself no other church can claim this

I don't think Catholics follow a very pure church. The Word of God does not agree with many of their rituals, such as works salvation, and other things.

"Gott ist tot."