It is narrated from Humaid bin Abdur Rahman that he heard Muawiyah bin Abi Sufyan (may Allah be pleased with him) in the year he performed Hajj, while he was delivering a sermon from the pulpit. He said: O people of Madinah! Where are your scholars? I heard the Messenger of Allah (ﷺ) on this very day, the Day of Ashura, say: "Fasting on this day has not been made obligatory by Allah upon you, but I am fasting. Whoever among you wishes may fast, and whoever wishes may break his fast."
Hadith Referenceمسند الإمام الشافعي / كتاب الصيام / 631
Hadith Takhrijاخرجه البخاري، الصوم، باب صوم يوم عاشوراء (2003) ومسلم، الصيام، باب صوم يوم عاشوراء (1129)۔