Does Josephus have anything to say about the Jewish high priest Josef Ben Caiaphas. after the crucifixion of Jesus Christ?

Josef Ben Caiaphas was the Jewish high priest during the time of Jesus’ ministry and for a few years afterwards. He was a strong opponent of Jesus and His message. Acts 4:1-22 informs us that Caiaphas continued to persecute the followers of Christ, being present at the trial of Peter and John. He is believed to have been born around 14 B.C. and died a few years after the crucifixion of Jesus. One source says he died in Crete and was buried in HaShalom Forest (Yaldei Israel Garden), Jerusalem. I would like to know if Josephus has any additional information about Caiaphas after the crucifixion of Jesus and up to the death of Caiaphas.