Well, first off it isn't an adverb. I'm not sure if you tagged the question yourself or if somebody did it for you, but it is indeed a preposition.
Otherwise, your example sentence is not incorrect, but it's also not the most natural phrasing. Most speakers would be more likely to say "What about the book under that one?" The prepositions "under"/"underneath," and "below" are fairly similar in their dictionary meanings, but are generally used in different ways.
Under is used when something is directly underneath another object, especially if it's being covered or hidden. A man would conceal a weapon under his coat, during a storm you may hide under a table, or perhaps you could drop your keys and lose them under the seat.
Below, on the other hand, simply indicates relative position and is more likely to be used when the two things in question are not immediately next to each other. Submarines cruise around below the surface of the water, my friend lives in an apartment a few floors below mine, and the molten core of our planet is far below the surface.
Although those are examples in which below is preferred, you can usually use under instead without sounding at all unnatural. The reverse is not always true. So, when in doubt, stick with under. Learning to use below in a sentence which sounds natural to native speakers is a skill that will come with time.
A brief note: Below is also used when imagining a sort of.. non-physical "vertical scale" rather than talking about actual positions. I could say a family lives below the poverty line, that the temperatures tonight may drop below freezing, or that a person is of below average intelligence. In this context it would be very bizarre to use under instead.