AFDHALIYYAT or Superiority in lslam means "to deserve more THAWAAB or Reward before Allah because of good deeds."
All Muslims agree that this Superiority cannot be decided by our own views or outlook and that there is no way to know it except through Quran and/or Hadeeth. Imam Ghazali (the famous Sunni scholar) has written: "The Reality of superiority is what is before Allah; and that is a thing which cannot be known except to The Holy Prophet(saww)".
Most of our Sunni brethren believe that the superiority was according to the sequence of the Caliphate, i.e., Abu Bakr was supreme-most, then Umar, then Uthman, then Ali Ibin Abe Taleb(as).
But this belief is not based upon any proof, nor was it the belief of all the Sunnis of early days.
Looking at the time of the Holy Prophet, we find that such respected companions as Salman Farsi, Abu Dhar Ghifari, Miqdad Kindi, Ammar bin Yasir, Khabbab bin Arrat, Jabir bin Abdullah. Hudhaifa Yamar.i, Abu Said Khudri, Zaid bin Arqam and many others, believed that Ali(as) was the Supreme most amongst all the Ahlul-Bait and companions.
Imam Ahmad bin Hanbal was once asked by his son about his views on the subiect of 'Superiority.'
He said: "Abu Bakr and Umar and Uthman." His son asked, "And what about Ali bin Abi Talib?"
He replied: "He is from Ahlul Bait. Others cannot be compared with him."
Ubaidullah Amritsari writes in his famous book 'Arjahul-Matalib' (p. 112):
"As 'Superiority' means 'having more Thawaab,' its proof can be known only from the AHDEETHS or Traditions of The Holy Prophet and if there are conflicting traditions then the better traditions should be accepted and strong traditions should bc differrentiated from weak ones.
Allama Ibn Abdil-Bar writes in his book 'Al-Istiab' about the Ahadith (traditions) which have been narrated about superiority of Ameerul-Mumeneen Ali: Imam Ahmad bin Hanbal, Qadhi Ismail bin Is'haq, Imam Ahmad bin Ali bin Shuaib Nasai and Hafidh Abu Ali Nishapuri have said, "There have not come 'Ahadith' with good, 'Asnaad' about virtue, of any of the companions as many as have been narrated on the virtues of Ali bin Abi Talib."
"Furthermore if we look at the exclusive virtues of Ameerul-Mumeneen Ali (a.s.) and think about those things which caused him to gather most rewards before Allah, we will have to admit that only he was the Supreme-most after the Holy Prophet." (Page 12).
That author was him-self a Sunni and has discussed this matter in detail in his above-mentioned book in the 3rd chapter beginning from page 103 and ending on page 516.
Obviously, I cannot give here even a short list of the Ayals and Ahadith concerning the Alldhaliyyat (superiority) of Ali(as).
Suffice it to say that there are at least 86 Ayats in the Quran extolling the virtues of Ali bin Abi Talib(as) and Ahaditll on this subjcct cannot be counted.
Thus, it is abvious even to a casual observer that Al-Imam Ali(as) was the Supreme most of all the Muslims after The Holy Prophet(saww).