Were the Jews right in accusing Jesus of claiming to be God? I was once asked this question by a Jehovah Witness to prove if the Jews understood that Jesus was claiming to be God. I affirm that they did while the Jehovah Witnesses deny it. 

Related question here
I'm going to approach this by saying the following. Whether or not the Jews are correctly or incorrectly understanding Jesus is not the issue. The issue is what was it that Jesus "SAID" that caused the Jews to say He was claiming to be God? 

John 5:16, "And for this reason the Jews were persecuting Jesus, because He was doing thins on the Sabbath." What Jesus did was heal on man on the Sabbath. Jesus says at John 5:17, "My Father is working until now, and I Myself am working." 

John 5:18, "For this cause therefore the Jews were seeking all the more to KILL Him, because (or why?) He not only was breaking the Sabbath, but also was calling God His own Father, making Himself equal with God." 

Jesus claimed to be the Son of God in the sense that no other believer is of God's essence. Look what Jesus says at Luke 2:49 when He was a boy. "Why is it that you were looking for Me? Did you not know that I had to be in MY FATHER'S HOUSE?" 

What did Jesus say at John 8:58 that upset the Jews? "Truly, truly, I say to you, before Abraham was born, I am." Jesus was saying to the Jews that before Abraham's existence He himself was existing. This is also confirmed at John 1:15 by John the Baptist. "John bore witness of Him, and cried out, saying, "This was He of whom I said, He who comes after me has a higher rank than I, FOR HE EXISTED BEFORE ME." 

So how did the Jews reply to what Jesus stated, "Therefore they picked up stones to throw at Him; but Jesus his Himself, and went out of the temple." Did you notice Jesus made His statement right there in the Temple.

How about what Jesus says at John 10:30, He literally says in the Greek, "I and the Father WE are one." Jesus distinguishes the "I" from the "Father" and uses the plural verb "are" denoting "we are." Asserting their unity of essence or nature as identical. Hence John 10:31, "The Jews took up stone AGAIN to stone Him."

The Jews understood Jesus correctly. There could be no mistake about His meaning. "Again" refers to John 8:59 at which time the Jews also attempted to stone Him for blasphemy. 

At John 19::7, "The Jews answered him, "We have a law, and by that law He ought to die because He made Himself out the Son of God." Matthew's trial record gets into more detail than the trial record here at John 19. 

The high priest Caiaphas at Matthew 26:63 ask Jesus a question? "I adjure You (swear to us) by the living God, that You tell us whether You are the Christ, the Son of God?" Caiaphas was clearly asking if Jesus was ONE person; "The Christ, the Son of (God)." Obviously Caiaphas did not believe that Jesus was "The Christ the Son of (God)"; it was a rhetorical question intended to trap Jesus into committing blasphemy. 

Jesus, calling Himself the Son of God is not blasphemy because He really WAS the Son of God. This is confirmed or proved by multiple Scriptures. Notice also how the the claim "Son of God," "equal to God," "making Yourself out God" are used interchangeably by the Jews. The high priest Caiaphas finally says at Matthew 26:65, "He has blasphemed! What further need do we have of witnesses? Behold, you have now heard the blasphemy."  

In conclusion, I find that there is an abundance of evidence that the Jews knew exactly that Jesus was clearly claiming to be God. Moreover, there is clear evidence throughout the New Testament that others stated He was God who were Jews as well.

As a side note! I could have proved the Jews knew Jesus was claiming to be God by writing the following 16 words or so and calling it a day. "If the Jews misunderstood Jesus, why did they bring up the Law at John 19:7?" The law that Jesus "supposedly" broke can be found at Leviticus 24:16. Bottom line, the Jews did not believe Jesus Christ.  

The following is from "Jews For Jesus." https://jewsforjesus.org/publications/issues/issues-v14-n02/the-claims-of-jesus/

This is another site that backs up what Jesus was claiming. https://www.oneplace.com/ministries/bible-answer-man/read/articles/did-jesus-claim-to-be-god-by-hank-hanegraaff-8825.html