adverb
The prepositional phrase is "by my aunt". It begins with the preposition "by" and ends with the object of the preposition "aunt". An adjective is a word that describes a noun. This prepositional phrase does not describe a noun. If it did you'd be able to say "The coat is by my aunt". This is not the same meaning. An adverb describes a verb. In this case "by my aunt" describes the verb sent because it tells where the coat was sent.
