What is equivalent resistance equation in this case?
we know that A is connected in parallel with B and also A is connected in series with C.

This isn't possible.
When we say &quot;A is in parallel with B&quot; we mean that each end of A is connected to one of the ends of B.
And when we say &quot;A is in series with C&quot; we mean that one end of A is connected to one end of C with nothing else connected at that same point.
So if we have A and C in series, and then connect B in parallel with A, then A and C are no longer in series.
Edit
In comments you clarified your arrangement is like this:

and current can't flow sideways.
In that case, A and C are in series. B is in parallel with the combination of A and C.
So the total resistance is given by
$$R=\frac{R_B(R_A+R_C)}{R_B+(R_A+R_C)}.$$
In the real world, assuming that current can't flow sideways might be leading you to an inaccurate estimate of the resistance.