Is there ASS congruence condition in maths?

The answer is Yes and No both!

In the condition ASS, expand it as Angle-Side1-Side2. Now, Two triangles are said to be congruent if and only if there is only a single triangle which can be constructed through those given conditions.For e.g. in SSS congruency only a single triangle can be constructed through given three sides in the congruency condition.

Here, if a triangle is constructed with a base side(Side1) and base angle (Angle), then the condition is based on the length of the third element (Side2). If side 2 is longer than side1, then two triangles are possible, but not if side2 is longer than Side1.

So, it depends on on second Side of the congruency condition.