Story of Mu'aawiyah's letter to Byzantine Emperor
14-1-2017 | IslamWeb
Question:
Assalaamu alaykum, dear Scholars. What is the source of the quote below given that this quote is highly shared on social media blogs and social sites? Is the quote below found in any authentic books of the Sunnah, and what is its authenticity?Your assistance in the matter will be highly appreciated.
The quote goes as follows:
Ceasar of the Romans to Mu'awiyah: We know what occured between you and 'Ali (Ibn Abi Talib), and we see that you are more worthy of the Khalifah, so if you order me, I will send you an army that will bring you the head of 'Ali.
From Mu'awiyah to Heraql: Two brothers dispute and what is it to you to enter between them? If you are not silent, I will send you an army that starts with you and ends with me and that will bring me your head so I can gift it to 'Ali.
Answer:
All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
After careful research, we could not find any basis for this report. It seems that it is one of the stories that are related in sermons and speeches without any chain of narration. However, among what historians recounted about Mu’aawiyah is what Ibn Katheer 
mentioned in Al-Bidaayah wa An-Nihaayah:
"The Byzantine Emperor had great hopes of attacking and defeating Mu’aawiyah after the latter had instilled fear in him and humiliated him and vanquished his troops. When the Byzantine Emperor saw that Mu’aawiyah was preoccupied with fighting ‘Ali, he approached some cities (on the border) with a huge army, filled with hope of victory. So Mu’aawiyah wrote to him saying, 'By Allah, if you do not desist and go back to your land, O cursed one, I shall reconcile with my cousin and we will unite against you, and I shall certainly expel you from all of your land! I shall keep pursuing you, and the earth, vast as it is, will be straitened for you.' At that, the Byzantine Emperor was scared off and abandoned his plans; he sent word seeking a peace treaty."
Allah knows best.