The correct option is D any
In the given sentence we want to tell that it doesn't matter which branch of your bank you can approach, to deposit your money. So, 'any' is the right option, as here 'any' means one among many, and it doesn't matter which. So, option D is correct.
Option A neither is incorrect, because it is used to refer to two things and it would mean there is no bank that you can approach.
Option B few and some are used to refer to plural nouns, whereas here the noun 'branch' is singular.