The hadith is in Al-Hakim, and Mustadrak, by Ali may Allah be pleased with him. It basically says that the sufyani will be descendant of Khalid bin Yazid bin Abi Sfyan, he will emerge in Damascus, and he will kill many and the killing will be so bad that it will get to a point were women will be sliced open and the infants in them will be killed. The Hadith goes on, it is long, but I wonder what is the authenticity of it.
According to Shia Islam Altough there are some hadith saying Sufyani is not a specific person and is a system and for each revolution is a sufyni but still there are some hadith saying Sufyani of time of Mahdi a.s. is descendant of Abi Sfyan. for example this hadith from Imam Sadiq a.s.:
About Sufyani there are many hadith but not all of them are considered authentic. there are some researchers dedicated to researches about ends of time and movement of Imam Mahdi a.s. and its signs. they say there are near 1000 signs mentioned in ahadith about signs of start of movement of Imam Mahdi a.s. that more than 950 of them have happened true until now. Ali Al-Kourani is a great scholar who has spend many years for research among dfferent hadith regarding the appearance of Imam Mahdi and has written a famous book based on his researches and determining authentic and non autenthic hadith. his book is called Epoch of Appearance ('Asr zohor).
He says in this book that the movement of Sufyani will be after an earthquake in Damascus with 100,000 being killed in it and so any movement in Damascus before this earthquake can not be considered as movement of Sufyani but current conflicts in Syria can be introductory steps of it. (taken from this Reference. you can read this Persian language page using Google translate.)
References and more study: