“But after the term of seventy years’ captivity under the Babylonians, Cyrus, king of Persia, sent the Jews from Babylon to their own land again, and gave them leave to rebuild their temple; at which time Jesus, the son of Josadek, took the high priesthood over the captives when they were returned home. Now he and his posterity, who were in all fifteen, until king Antiochus Eupator, were under a democratic government for four hundred and fourteen years; and then the forementioned Antiochus, and Lysias the general of his army, deprived Onias, who was also called Menelaus, of the high priesthood, and slew him at Beroea; and driving away the son [of Onias the third], put Jaceimus into the place of the high priest, one that was indeed of the stock of Aaron, but not of that family of Onias. (ie Zadok) On which account Onias, who was the nephew of Onias that was dead, and bore the same name with his father, came into Egypt, and got into the friendship of Ptolemy Philometor, and Cleopatra his wife, and persuaded them to make him the high priest of that temple which he built to God in the prefecture of Heliopolis, and this in imitation of that at Jerusalem; but as for that temple which was built in Egypt, we have spoken of it frequently already. Now when Jaceimus had retained the priesthood three years, he died, and there was no one that succeeded him, but the city continued seven years without a high priest. But then the posterity of the sons of Asamonaeus, who had the government of the nation conferred upon them, when they had beaten the Macedonians in war, appointed Jonathan to be their high priest, who ruled over them seven years. And when he had been slain by the treacherous contrivance of Tryphon, as we have related some where, Simon his brother took the high priesthood; and when he was destroyed at a feast by the treachery of his son-in-law, his own son, whose name was Hyrcanus, succeeded him, after he had held the high priesthood one year longer than his brother. This Hyrcanus enjoyed that dignity thirty years, and died an old man, leaving the succession to Judas, who was also called Aristobulus, whose brother Alexander was his heir; which Judas died of a sore distemper, after he had kept the priesthood, together with the royal authority; for this Judas was the first that put on his head a diadem for one year.
And when Alexander had been both king and high priest twenty-seven years, he departed this life, and permitted his wife Alexandra to appoint him that should he high priest; so she gave the high priesthood to Hyrcanus, but retained the kingdom herself nine years, and then departed this life. The like duration [and no longer] did her son Hyrcanus enjoy the high priesthood; for after her death his brother Aristobulus fought against him, and beat him, and deprived him of his principality; and he did himself both reign, and perform the office of high priest to God. But when he had reigned three years, and as many months, Pompeius came upon him, and not only took the city of Jerusalem by force, but put him and his children in bonds, and sent them to Rome. He also restored the high priesthood to Hyrcanus, and made him governor of the nation, but forbade him to wear a diadem.This Hyrcanus ruled, besides his first nine years, twenty-four years more, when Barzapharnes and Pacorus, the generals of the Parthians, passed over Euphrates, and fought with Hyrcanus, and took him alive, and made Antigonus, the son of Aristobulus, king; and when he had reigned three years and three months, Sosius and Herodes besieged him, and took him, when Antonius had him brought to Antioch, and slain there.
Herodes was then made king by the Romans, but did no longer appoint high priests out of the family of Asamonaeus; but made certain men to be so that were of no eminent families, but barely of those that were priests, excepting that he gave that dignity to Aristobulus; for when he had made this Aristobulus, the grandson of that Hyrcanus who was then taken by the Parthians, and had taken his sister Mariamme to wife, he thereby aimed to win the good-will of the people, who had a kind remembrance of Hyrcanus [his grandfather]. Yet did he afterward, out of his fear lest they should all bend their inclinations to Aristobulus, put him to death, and that by contriving how to have him suffocated as he was swimming at Jericho, as we have already related that matter; but after this man he never entrusted the priesthood to the posterity of the sons of Asamonaeus. Archelaus also, Herodes’s son, did like his father in the appointment of the high priests, as did the Romans also, who took the government over the Jews into their hands afterward. Accordingly, the number of the high priests, from the days of Herodes until the day when Titus took the temple and the City, and burnt them, were in all twenty-eight; the time also that belonged to them was a hundred and seven years. Some of these were the political governors of the people under the reign of Herodes, and under the reign of Archelaus his son, although, after their death, the government became an aristocracy, and the high priests were entrusted with a dominion over the nation. And thus much may suffice to be said concerning our high priests.- Antiquties 20:10
Backing up a bit we can narrow in on the rapid turnover of priests under the administration of Gratus (15-26 ad) in the years leading up to Messiah’s ministry.
He (Tiberius) was now the third emperor; and he sent Valerius Gratus to be procurator of Judea, and to succeed Annius Rufus. This man deprived Ananus of the high priesthood, and appointed Ismael, the son of Phabi, to be high priest. He also deprived him in a little time, and ordained Eleazar, the son of Ananus, who had been high priest before, to be high priest; which office, when he had held for a year, Gratus deprived him of it, and gave the high priesthood to Simon, the son of Camithus; and when he had possessed that dignity no longer than a year, Joseph Caiaphas was made his successor. When Gratus had done those things, he went back to Rome, after he had tarried in Judea eleven years, when Pontius Pilate came as his successor.“- Ant 18:2:2
So it is appears that the Zadokites lost the priesthood with the Syrian expulsion of Onias III. Interstestingly it has been suggested by scholars that this is what is referenced in Daniel 11:22 as the over throwing of the ‘Prince of the Covenant.’
Following the Maccabean revolt the Hasmoneans held the priesthood and eventually ruled as kings til infighting brought the Romans into the narrative, appointing Herod king. With his anxious attempt to consolidate power he married in then killed off any possible contestants to the throne.
By Yeshua’s coming of age the Priests had become engrossed in the politics of obtaining and holding office via cooperation with Rome. The status was granted and revoked at the whim of governers, irrespective of lineage or Judaic custom. Those who wished to excel straIned to maintain the peace against nationalist factions as tensions steadily increased. The stage was set for a showdown when Messiah came riding into town, the Son of David, king and priest according to the order of Melchizedek.