Sussex Police has launched an appeal for information following the incident, which happened during the night.
Police said officers responded to a fight between two men in Robertson Street, the pedestrianised area between HSBC bank and Yates bar, at around 3am on Sunday, July 25.
A 28-year-old man was arrested at the scene on suspicion of affray, assault on a restrained male and assaulting a police officer.
Police said a 20-year-old man was also arrested on suspicion of affray and assault on a restrained male.
Sussex Police confirmed that it has since been established one of the men suffered a fractured jaw and skull in the altercation.
Anyone who witnessed this incident or has any information is asked to contact police online or by calling 101 quoting serial 0247 of 25/07.