The issue of authority is an involved and complex one in all religions and Islam is no exception to this. According to the Qur’an, authority belongs first and foremost to Almighty God: Rabb al-‘alamin (the Lord of the Worlds). He bestows it upon His prophets, the final one of whom is Prophet Muhammad, who is designated the Rahma l’il-‘alamin (mercy to the worlds). It is then transmitted to those in authority who, according to Shi‘i interpretation, are the imams from the progeny of the Prophet through Imam ‘Ali and the Prophet’s daughter, Fatima. This, according to Shi‘i interpretation, is referred to in the following verse of the Qur’an: “Ya ayyuhal ladhina amanu ati‘ullaha wa ati‘urrasul wa ulil amri minkum.” (4:59) (O ye who believe! Obey God and obey the Messenger and those vested with authority from among you.)
The notion of authority is fundamentally linked to establishing the right guide who has the requisite knowledge and the legitimacy to interpret the Qur’an across the span of time.
via The Institute of Ismaili Studies – Approaches to the Qur’an.
Ismailimail 
Yes According to the saying of our Holy Prophet ” Ali is from me and i am from Ali”, ” I am the city of knowledge and Ali is its gate” From the above and many other saying of our Holy Prophet it becomes clear the authority.
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