The correct options are
A by
B on
The preposition ‘by’ is used to indicate that an object is ‘by the side of’ or ‘next to’ something else. In the given sentence, the taxi stops close to the side of the road, therefore ‘by’ is apt. In addition to this ‘on’ can also be used in the given sentence, because ‘on’ is used to indicate that something is placed on top of or above a surface or on something that we perceive as a line such as a road or a river. Therefore options A and B are correct. The preposition ‘in’ is used to indicate a city or country. Since the sentence clearly states that it is the side of the road, ‘in’ can’t be used. Hence option C is incorrect. Whereas, ‘under’ is used when something is vertically below another object. The taxi here is not below anything, it is over the road. Thus option D is incorrect.