Once captured, all Gospels record that Jesus was questioned by the High Priest. Two of the Gospels (Matthew and John), mention the high priest by name – Caiaphas.
From Josephus we know that the full name of Caiaphas was Joseph Caiaphas (Antiquities of the Jews, 18.2.2/35; 18.4.3/95), and that apparently he was in seat between 18 and 36 AD.
Catholic tradition argues the estate of Caiaphas the High Priest was on the eastern slopes of Mount Zion, in an area known as Peter in Gallicantu (Peter of the Cockcrow). Visitors to the site are presented with a set of underground caves, one of which is arguably the pit where Jesus was kept while being interrogated by Caiaphas.
However from an archaeological point of view, this “prison” seems to really be a first century AD Jewish ritual bath (miqveh) which was later deepened and turned into a cistern.
The other finds from the site indicate the landlord was wealthy, but there is no conclusive evidence to suggest he was a High Priest, nor that the pit was used to detain anyone. Furthermore, Byzantine sources describe the home of Caiaphas as being elsewhere, on the top of Mount Zion, near Hagia Zion church. Remains of a wealthy residential area from the first century AD were recovered close to Hagia Zion church in the 1970s, but they did not bear any finds to suggest this was necessarily the estate of the High Priest.
Clearer archaeological evidence of Caiaphas surfaced by surprise in 1990, during a salvage excavation on a mountain ridge south of the old city of Jerusalem. As a new road was being constructed in that area an ancient burial cave was accidentally discovered. Archaeologist Zvi Greenhut of the Israel Antiquities Authority was called to the scene, and he recovered in the cave 12 ossuaries (secondary burial bone boxes). One of the ossuaries was very ornate and bore two inscriptions on its side, both saying “Yoseph of Caiapha” (Joseph of Caiaphas). Inside the ossuary, among others, were the bones of a male in his sixties. Being so, it seems possible that this was the ossuary used for the secondary burial of Caiaphas, the High Priest who questioned Jesus.
This ossuary today is on permanent display in the Israel Museum. A photo and a review of it can be seen here.
One would not expect the find of another ossuary that could be connected to Caiaphas, but archaeology has its surprises, and just a few months ago another ossuary related to Caiaphas was purchased by the state of Israel.
An ossuary purchased recently by the state of Israel is less ornate then the Caiaphas ossuery, but is inscribed as belonging to “Miriam, daughter of Yeshua“. Her grandfather, according to the inscription, is – “[Priest] CAIPHAS“.