Is the aforementioned hadith authentic, regarding Aisha's question to the Prophet, peace and blessings be upon him, about which of his wives was dearest to him, and his giving each of them a ring?

A Hadith with this wording or meaning has not been found in the books of Sunnah, which indicates that it is fabricated. It is impermissible to circulate Hadiths found online except after verifying their authenticity, because the Prophet, may Allah bless him and grant him peace, warned against narrating a false Hadith from him, saying: "Whoever narrates a Hadith from me which he considers to be false, then he is one of the liars." He also said: "It is enough sin for a man to narrate everything he hears."