Did James and John, the Sons of Zebedee, Die for the Gospel?

In Matthew 20, Jesus confirms that his cousins, James and John, will suffer, and possibly die, for his sake. This raises the question of whether we have any historical documentation about the deaths of James and John.

With regard to James, the book of Acts, chapter twelve, actually records his death around the year AD 44.

About that time Herod the king laid violent hands on some who belonged to the church. He killed James the brother of John with the sword, and when he saw that it pleased the Jews, he proceeded to arrest Peter also.

Given that there are several Herods mentioned in the Bible, which Herod killed James? According to gotquestions.org,

Herod Agrippa I was the grandson of Herod the Great (Acts 12). It was he who persecuted the church in Jerusalem and had the apostle James, the brother of John and son of Zebedee, put to death by the sword. By the hand of Herod Agrippa I, James became the first apostle to be martyred.

With regard to John, the historical record is less clear. According to ccel.org, here is the most plausible account of what happened to John:

According to John’s Gospel (19:26-27), it was probably John who took Mary, the mother of Jesus as his adopted mother. He preached in Jerusalem, and later, as bishop of Ephesus, south of Izmir in western Turkey, worked among the churches of Asia Minor. During the reigns of either Emperor Nero (AD 54-68) or Domitian (AD 81-96), he was banished to the nearby island of Patmos, now one of the Greek islands in the Aegean Sea. He was subsequently freed and died a natural death at Ephesus c AD 100.

John likely was assigned to slave labor in the mines of Patmos, so he did indeed suffer greatly. There is also a church tradition which claims that, at one point, John was thrown into a basin of boiling oil.

Both brothers, then, suffered greatly for proclaiming the gospel. James was the first apostle to be martyred and John, although he lived several more decades than his brother, was banished to work the mines on the island of Patmos.