In Matthew 26:63-64, does the high priest think that the Messiah is Son of God? Matthew 26:63-64 NIV:


  The high priest said to him, “I charge you under oath by the living God: Tell us if you are the Messiah, the Son of God.” “You have said so,” Jesus replied.


So do Jews believe that the Messiah is to be the Son of God or is it a later Christian invention?

Jews tend to think that christians commit idolatry. However, merely believing that Jesus is the messiah is not idolatry. Rabbi Akiva did that too to someone else.

The question is about the idea whether messiah is the Son of God or not. If even the high priest, and Peter, believed that, then it'll be very interesting. Peter, a jew, also equated Son of God with Messiah when Jesus asked "Who do you think I am?"

This question is not about divinity of Jesus. That will be a different question. The question is whether the idea that messiah is a Son of God (perhaps in some lesser sense) originate out of judaism.
Several Second Temple documents — and not just the Christian tradition — reflect the hope that God will re-establish the Israelite monarchy. This was often based on the promises God makes to David in 2 Sam 7, which state that his son Solomon:


Will build the Temple.
Will become God's son.
Will have a throne established forever.


This makes excellent sense of the fact that the High Priest, in the passage you are asking about, moves directly from questions about Jesus's relationship to the Temple to a question about whether Jesus is God's son: both questions were attempts to determine whether Jesus saw himself as a fulfillment of 2 Sam 7. So when the High Priest asked if Jesus was God's son, he meant, “do you think God has adopted you as a son to rule over his people Israel, like he adopted Solomon as his son?”