One example of special forces in Rome would be the Lictor.
The lictor was a member of a special class of Roman civil servant, with special tasks of attending magistrates of the Roman Republic and Empire who held imperium.
The lictor's main task was to attend as bodyguards to magistrates who held imperium: consuls, praetors, dictators and curule aediles; the dictator's deputy, the magister equitum ("Master of the Horse") was also escorted by six lictors. Men with proconsular or prepraetorian imperium were also entitled to lictors. They carried rods decorated with fasces and, outside the pomerium, with axes that symbolized the power to execute. They followed the magistrate wherever he went, including the Forum, his house, temples and the baths. If there was a crowd, the lictors opened the way and kept their master safe. They also had to stand beside the magistrate whenever he addressed the crowd. Magistrates could only dispense their lictors if they were visiting a free city or addressing a higher status magistrate. Lictors also had legal and penal duties: they could at their master's command arrest Roman citizens and punish them.
Although they were not special forces in essence of elite soldiers, there were certainly a special class of citizen.
As well, this may be a little past the time you're looking for, but in the time of the Later Eastern Roman (Byzantine) Empire, the Varangian Guard were elite Russian Forces employed to protect the Emperor.