Ali bin Abu Taleb Mosque is located approximately 300m to the north west of Al-Ghamama (The Cloud) Mosque. Perhaps it was named after Ali bin Abu Taleb, God bless him, because he prayed the Eid for the people when Uthman, God bless him was besieged.
Ali, God bless him, is not known to have prayed the Eid in Medina during his term as Caliph. It is not believed that Ali, God bless him, had prayed in a spot where the Prophet (PBUH) had not prayed.
In order to know all the holy sites the foot of the Prophet (pbuh) had treaded on; download Following Prophet Footprints application which supports navigation maps without an internet connection.