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.