Since the four gospels of Christ were written Satan has attempted to lead mankind away from the saving grace of God. Failing that, Satan has tried to convince man that the authorship of the gospels is in question. For 2000 years critics have tried to discredit the Bible and failed. The evidence is rock solid that the gospels of Matthew and John were written by the Apostles John and Matthew.
The authorship of the gospel of Luke is the best documented gospel because in it the writer identifies himself as Luke, a Gentile physician and disciple of the Apostle Paul. Luke makes clear he did not know Jesus personally but is truthfully reporting eyewitness testimony of the Apostle Paul and his investigation into the life and teachings of Jesus Christ. Early church fathers like Origen, Irenaeus and Tertullian all confirmed Luke penned the gospel of Luke in Greek to the Gentiles after Mark and Matthew were written but sometime before the death of Paul in Rome making it prior to 66 AD.
The Apostle John wrote the gospel bearing his name last and had read the other gospels before he wrote his gospel. The Apostle John was illiterate so he dictated his gospel. The Apostle John was an eyewitness to the life and teachings of Jesus Christ and, as the beloved disciple of Jesus, was part of his inner circle and witness to things not widely known by the other gospel writers. The Apostle John attempted to fill in the information missing from the other gospels and to stress the divinity of Jesus. Early church fathers from all over the world such as Martyr, Irenaeus, Clement and Tertullian all wrote confirming the Apostle John wrote his gospel. There has never been any disputing who authored the four gospels of Christ, only the order in which they were written. The gospel of John was written last according to historical records.