What year did Saturday night masses start in the Catholic Church?

Sunday Masses celebrated on Saturday evening began after Vatican Council II. They were going with the old Jewish liturgical day, which begins at sunset the night before. In reality the Church has always done this, with the Holy Saturday Vigil Mass - the first Mass of Easter, although, over the centuries, it had gotten so moved up that it was being celebrated on Holy Saturday morning. This has been corrected, and the "vigil" spread to all Sundays in an effort to accommodate people who had to work on Sunday. It probably started in some Churches in the late '60's, and was widespread in the '70's.