This is a very well known narration from Sahih Muslim that says, when Moawiya bin Abu Sufyan used to appoint a Governor, he used to give orders to his Governors to curse on Imam Ali in mosques and public places. When he appointed Sa'ad bin ABi Waqas he ordered him to do such thing.
Sa,ad bin Abi Waqas said there are three virtues of Imam Ali I cannot do so, Please read those 3 promonent virtues of Imam Ali in this narration.
This is a very well proven fact (unfortunately) that Moawiya started cursing on Imam Ali in mosques (Friday and Eid sermons), It remained for many decays until the time of Umar bin Abdul Aziz (Ummayad caliph), he stopped it.
This is also a proven reality that along with cursing on Imam Ali (as) Moawiya fought war with Imam Ali, thousands of people got killed. We discussed these things in our articles, we cannot talk much in here about Moawiya's enmity with Imam Ali.
Please read next hadith from Sahih Muslim which is very important.