Jesus dealt with children of the devil:
Joh 8:44 Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.
The ones Jesus was talking to were the ones who call themselves Jews.
Rev 2:9 I know thy works, and tribulation, and poverty, (but thou art rich) and I know the blasphemy of them which say they are Jews, and are not, but are the synagogue of Satan.
There are Jews all around us today. They control most of the money in the world. They don't hide the fact, since they still call themselves Jews and don't believe Jesus is the son of God.
You're talking about the "mystery of iniquity".
Early in Israel's history the Canaanites crept in among them. God had told the children of Israel to destroy the seven specific peoples of the land of Canaan because of their iniquity, but also because the giants were there, and those hybrids were not part of God's plan. The Kenites of the land of Canaan especially crept in among Judah and became Israel's scribes (1 Chronicles 2:55). In Joshua 9, a group of Canaanites who feared destruction by Israel disguised themselves as travelers from a far off land. They made a pact with Joshua to dwell among the Israelites, and then it was discovered they were actually Canaanites. Joshua then made them bondservants. In Judges 2 & 3, God was angry with the children of Israel because they had not obeyed His command to wipe out all the Canaanites. So God said He would leave them among Israel to try Israel with.
In Solomon's days, the left-overs of the Canaanites were still among Israel as bondservants, hewers of wood and drawers of water. Some of them eventually became temple workers called Nethinims. And some of them would even creep into the priesthood (see Ezra 2).
Then there was the nation of Edom. Because they wouldn't allow the children of Israel to pass when they left Egypt to come into the lands of promise, God destroyed that nation. Many of the Idumeans thus became converted Jews dwelling among Judah. King Herod himself was a converted Jew of Idumean birth (Esau). So there's that group among today's Jews also.
Then the old nation of Khazaria converted to the Jew's religion long ago, and became religious Jews. Many of those wound up being the majority of the Ashkenazi Jews that migrated to Europe.
In the last verse of Zechariah 14, we are told then, in that future time, there will no more be the Canaanite in the house of God.
Thus the "synagogue of Satan" our Lord Jesus pointed to isn't simply about orthodox unbelieving Jews. It's more about the foreigners that crept in that God ordained to work the negative side of His plan. Per Paul in Romans 11, God put blindness on the majority of the 'authentic' Jews so The Gospel would go to the Gentiles. When that blindness is removed, they will believe on Jesus. But for the Canaanite crept in unawares, with their 'beast' nature, many of those likely won't convert to Jesus.
Jesus also showed His elect that He will make those of the "synagogue of Satan" to worship at the feet of His elect. So they will bow to Christ Jesus in the future during His Millennial reign, but they may not all believe to be saved. Yet that shows in Christ's future thousand years reign, it will be our job to teach them.
In summary then, those represent the "tares" in Christ's parable of the tares of the field. The good seed represent the good children of God. But the tares represent the children of the devil, his servants that were ordained to that condemnation per Jude 1. When the worker asked the master to harvest then before harvest time to get the tares out, the master said no lest you mistakenly reap some of the good wheat also. Instead wait until harvest time. That means it's not up to us to identity who the 'tares' are, as one deceived might be following them which otherwise would not (like Apostle Paul was once deceived against Christ). We are told to recognize the fruit.
That's who is in control of this world, except where God allows His servants to have power, like President Trump today. He represents the OT working of Jehu who cleansed Israel of a lot of the idols. That is why Satan's workers hate Trump so much.