In textbooks it’s taught that in parallel circuits the voltage across resistances is same as that of battery but after that we also read the concept of potential drop across resistances, which creates a confusion that how voltage across resistances is same as of battery after a potential drop.
The point of your question is hard to understand for me because I think you have a bit of a misunderstanding on the notions you are talking about. Before anything else, ask yourself those questions : "what does potential mean ?", and "what does voltage mean ?". Never try to understand a problem if this problem contains words that you can not define (=can not understand)
You will soon find that, by definition, potential drop = voltage. It's the same thing. They are both "across" the resistance, I do not understand why you talk about your resistance coming up "after" the potential drop.
Just review the fundamental definitions of the notions you qre trying to use, and it should start to make sense. Maybe you can come back with a better fromulation if you still have an issue after that
I think you are confusing where the "drop" happens. If you have a bunch of resistors in parallel, they all see the same voltage. However the battery also has an internal source resistance. That resistance (or impedance) is in series with the parallel resistors and that's where "voltage drop" typically happens.
If you have a 12V battery, you may only get 11.5V to the resistors since 0.5V are dropped at the internal source resistance. However, all parallel resistors would see the same 11.5V.
The more resistors you put in parallel, the higher will be the current that the battery needs to deliver, the more voltage will drop at the source resistance and the lower the voltage at the parallel resistors will be.