Assertion (A) : An electron on p-side of a p-n junction moves to n-side is called drifting of charge carriers across junction.

Reason (R) : Drifting of charge carriers reduces the concentration gradient across junction.

Both A and R are true, but R is the NOT correct explanation of A

The barrier potential develops a barrier field in the direction n to p side. This barrier field immediately pushes the electron towards the n- side and holes towards the p- side, and then a current is set up by the barrier field from n to p side. This current is known as drift current. 

It reduces the concentration gradient.