A verb is used to express an occurrence, action , or state. It is the grammatical centre of the predicate in a sentence.
An auxiliary verb is a verb which gives is used in the formation of tenses, moods, tones, etc.
A modal auxiliary verbis used to show a capability,necessity, possibility or willingness.
Option B is correct as the subject is singular and the sentence talks about possession.
Other options are wrong as the subject is not plural.
The correct answer is B)has.