See below "Excepts from 'The Trial of Jesus' "
Rabbinic Judaism rejects any connection with the trial of Jesus with or without a "sanhedrin". Modern Judaism is called Rabbinic Judaism and claims descent from the Pharisees, a group at odds with the Sadducees.
It is possible that the trial was as a Sadducean illegal court, or perhaps the details as we know them today are incomplete or inaccurate. Josephus (Ant. 20:9, etc) generally portrays the Sadducees as antagonistic to early Christianity, while the New Testament (John 3:2, Acts 5:34, etc) portrays Pharisees as being tolerant (see Acts 23:6 for both roles).
The role of the Sadducees in trying and executing early Christians is explicitly referenced in Josephus. In 62 CE the Jewish priest and Sadducee, Ananus, convened the Sanhedrin in his house and condemned Yaakov [James], half-brother of Yeshua, who is then summarily executed.[Josephus, ibid]
Excerpt from "The Trial of Jesus"
Excerpt from "The Trial of Jesus" by Douglas Linder of the University of Missouri-Kansas City School of Law:
Around 200 C.E., Sanhedrin becomes a technical term for a rabbinic court. A tractate in the Mishnah prescribes procedures the Sanhedrin is to use. The excerpts below, taken from the Mishnah Tractate, may shed light on the procedures used in the case of Jesus. One caution, however: the Mishnah was not compiled until 200, and it is therefore possible that some of the procedures and restrictions described in the Mishnah Tractate were not in force in the time of Jesus.
The gospel of John indicates that the Sanhedrin turned Jesus over to Pilate because it lacked the power to impose death: "Pilate said to them, 'Take him yourselves and judge him according to your law.' The Jews replied, 'We are not permitted to put anyone to death.'" The Mishnah, however, clearly shows that the Sanhedrin did have the power to impose death for certain crimes--at least sometime before 200 C.E. In particular, Mishnah Sanhedrin 6.1 to 6.4 specify the procedures for stoning. There is no evidence to suggest that the power did not exist in 30 C.E. On the contrary, there is evidence that the Romans preferred to leave as much power as possible to control religious crimes in the hands of Jewish authorities.