Let us examine the status of the Kohanim, the priests who functioned in the Temple and performed its rituals and ceremonies. All of this is described in detail in the Tannaitic literature. The priests who held the leading positions in the Temple and from whose number the High Priest was chosen, were descendants of the High Priest Tzadok who had been appointed Kohen Gadol by Solomon at the time of his coronation. All the Kohanim who served in the Temple since the time of Solomon were of the family of Tzadok.
After the destruction of the First Temple by the Babylonians in 586 B.C.E., this activity was interrupted and the Kohanim in exile had no priestly functions. But when the Temple was rebuilt during the days of Ezra and Nehemiah, the prieshood was restored to its position, and the same family, the descendents of Tzadok were reinstated in their positons. Yehoshua the High Priest mentioned in the book of the Prophet Zechariah assumed his position as High Priest in the restored Temple in Jerusalem.
Yehoshua ha-Kohen Ha-Gadol was a Zadokite; that is, a Sadducee. That was the name of the entire priestly family, descendants of Tzadok, who were in control of the Temple from its very beginning until the time of the Maccabean Rebellion. The Tzadukian priesthood was their family identity; the concept of Sadduceean religious philosophy in contrast to that of the Pharisaic had not yet developed, and the seed of the conflict that was ultimately to divide them and create the profound enmity between the two groups had not yet germinated.
There were other priestly families, groups whose names and identities are known to us. But these were Kohanim who had been removed from functioning in the Temple. One prominent family was that of the priests who were descendants of Abiathar, the Kohen Gadol who had been removed from his position because of his alliance with Adoniyahu, the older brother of Solomon, who was his rival in the struggle for succession to the throne of David.
The Kohen Tzadok was Solomon's partisan and he was elevated by the new king to the position of primacy. Abiathar was exiled from Jerusalem and settled in the town of Anatoth, some ten kilometers northeast of Jerusalem. While a Kohen and the ancestor of many Kohanim, none of them functioned in the Temple of Jerusalem, since that was exclusively the prerogative of the family of the descendants of Tzadok. The most prominent member of the descendants of Abiathar was Jeremiah the Prophet, one of the greatest of Israel's spiritual teachers, but never a functioning member of the Temple hierarchy.