There are two possibilities depending on where A is.
If A is on one side of both P and Q, then net force can be zero, only if one charge is higher and another smaller and both are oppositely charged. It will be possible when the charges A, P and Q are collinear.
Net force on A will be zero, if A is in between P & Q and they are both of the same polarity. ie., both positive or both negative. Here the to forces will be in opposite directions. Assuming that A, P, and Q are on the same straight line. Here is it possible that on e charge is higher than the other.