The correct option is
B Whose / is / our
The correct answer is Option B.
WHOSE means belonging to or associated with which person. It is used to ask about someone's relation. In the given sentence, the speaker wants to know who the child belongs to. Thus WHOSE is the correct answer.
IS is used the present tense and for a single person. In the given sentence the subject is a single child.
OUR is a possessive adjective. It describes a noun. OUR describes the yard i.e. who the yard belongs to.
Thus Option B is the correct answer.
The remaining options are incorrect because:
Option A: WHO'S is the contraction of WHO IS.
Option C: OURS is a possessive pronoun that is used in place of a noun.
Option D: ARE is used for plural subject, in the given sentence, the subject is a single person.