What do you call a quarter of an A4 sheet of paper?

A6.

The A series of paper is such that the next number up is half the size of the current number.

Thus 1/2 A4 is A5, 1/2 A5 is A6.

And 1/4 A4 is (1/2 (1/2 A4) which is 1/2 A5 which is A6