It is narrated from Sayyiduna Ali (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) himself used to fast on the day of Ashura and would also encourage others to do so.
Hadith Referenceمسند احمد / مسند الخلفاء الراشدين / 1069
Hadith Gradingحکم دارالسلام:حسن لغيره، وهذا إسناد ضعيف لضعف جابر الجعفي