The Core FourFour current players on the New York Yankees started their careers as Yankees in 1995. You might want to exclude Andy Pettitte as he took off to Houston for three years. That narrows it down to three players. Here is a list of when each player made their Major League debut that year. I don't know who was on the opening day roster. You decide.
Andy Pettitte made his Yankees debut on April 29, 1995
Mariano Rivera made his Yankees debut on May 23, 1995
Derek Jeter Made his Yankees debut on May 29, 1995
Jorge Posada made his Yankees debut on September 4, 1995