The correct answer is C. A participial phrase modifying me
Step-by-step explanation:
In grammar, words that derive from a verb and end in -ing can be either participial or gerunds and along with more words create a gerund or a participial phrase. But both gerund and participials have a different function, in the case of a gerund, this acts mainly as a noun, while in the case of participles these are words that act either as an adjective modifying a noun or as a verb. The sentence presented "My mother found me standing near the cookie jar" contains a word ending in -ing which is "standing" and this word mainly acts as an adjective because it describes the position of "me", therefore, this word is a participle, because the word acts as an adjective and not as a noun or verb and it modifies the word "me" and thus, the sentence contains a participial phrase modifying me.