Is it authentic that the Prophet (SAWW) said no one loves Ali (a.s.) unless believer and no one hates him unless hypocrite?
If yes then what is the reason of this? And is this said about any other Sahaba or only about Ali (a.s.)?
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Yes, it is accepted among Muslims that The Prophet (PBUH) had said that, and he did so only about Ali (AS). Ali (AS) was the first man to become a Muslim, even before Abu Bakr, and this is a proven fact in both Sunni and Shi’i sources.
قال علي والذي فلق الحبة وبرأ النسمة إنه لعهد النبي الأمي صلى الله عليه وسلم إلى أن لا يحبني إلا مؤمن ولا يبغضني إلا منافق
'Ali said: By the One Who split the seed and created the soul, the [unlettered] Prophet ﷺ, affirmed to me: "No one loves me except a believer and no one hates me except a hypocrite."
— Sahih Muslim, The Book of Faith, Chapter: Evidence that love of the Ansar and Ali (r.a.) is a part of faith and a sign thereof; Hating them is a sign of hypocrisy - (sunnah.com) ; ( Darussalam  131 - (78) )
قال علي: والله إنه مما عهد إلي رسول الله - صلى الله عليه وسلم - أنه لا يبغضني إلا منافق، ولا يحبني إلا مؤمن
'Ali (RA) said: By Allah, one of the things that the Messenger of Allah (ﷺ) promised me was that no one would hate me except a hypocrite and no one would love me except a believer.
عن علي، قال لقد عهد إلي النبي الأمي صلى الله عليه وسلم أنه لا يحبك إلا مؤمن، ولا يبغضك إلا منافق
Narrated 'Ali: The Prophet (ﷺ) - the Unlettered Prophet - exhorted me (saying): 'None loves you except a believer and none hates you except a hypocrite.'