What is the correct pronoun to complete the sentence: That beautiful painting used to belong to my sister and __________.

In this sentence, the correct pronoun to complete the phrase is "me." The structure of the sentence implies that the speaker is referring to themselves in an object position—specifically as the recipient of the ownership described.

When discussing ownership or association with someone, when it involves the speaker (the person using the pronoun), "me" is the appropriate choice after a conjunction. The phrase "my sister and me" correctly uses the object pronoun to indicate that the beautiful painting used to belong to both individuals.

Using "I" would suggest a subject position rather than an object, which does not fit in the context of this sentence. "Mine" is a possessive pronoun that does not fit grammatically in the sentence structure as it would require rephrasing. "Myself" is a reflexive pronoun and also does not fit here, as it doesn't suit the context of ownership between the speaker and their sister.