is there is any AAA congruence criterion?
No, there is no congruency rule as AAA because:
If all the angels of tw0o triangles are same it doesnt makes them congruent as their sides may increase or decrease without disturbing the measures of the angles.
We can take two equilateral triangles. both of them would have all their angles 60 degree. One of the triangle could have all its sides measurinng 5cm and the other could have all its sides measuring 7cm.
in this case both will have al their angles equal but not the sides therefore you cannot determine whether two triangles are congruent by just knowing that all there angles are equal.