There is no one way to hold a putter correctly. There is a suggested way which is most common and used by many elite golfers but there are other acceptable variations which work well. The Fundamentals of Putting explains the preferred gripping method which is the reverse overlap.
This is with the right hand low – for right handers – and the left hand above it with the index finger of the left hand overlapping the pinky of the right hand.
Whatever your gripping style the putter must be held with the minimal pressure. If you tighten down on your grip you will introduce tension into your forearms which detrimentally affects the rhythm or tempo of the stroke.