Is the Hadith: "The Messenger of Allah (peace be upon him) smiled one day and said: 'Are you laughing at me, O Messenger of Allah?' because I am shorter in stature than Umar. So the Messenger of Allah said: 'A time will come when they will differentiate between you, O Ali.' Ali said: 'If I were in that time, I would cut off their heads,'" an authentic Hadith?

The statement mentioned in the question is not found in the books of Sunnah (definition) or in books of fabricated or weak hadiths, which indicates that it has no basis. The alleged laughter of the Prophet, peace and blessings be upon him, in this narration is inappropriate, as the Prophet would not laugh at someone's short stature. Rather, he forbade mocking people's creation, and he strongly condemned Aisha when she pointed out Safiyyah's short stature, and he disapproved of the Companions' laughter at the thinness of Ibn Mas'ud's shins. Laughing at a person's physical creation is considered forbidden mockery, and if it is due to people differentiating between Ali and Umar, then this is a sad matter, not a laughable one.