North Yorkshire Police said a group of men were seen fighting on Baxtergate just after 6pm on December 31.
Two of the men were knocked unconscious and one was taken to hospital by ambulance.
Police are asking members of the public to get in touch if they recognise the people in the images as they believe they will have information that will help the investigation.
Contact North Yorkshire Police on 101, quoting reference number 12180242405
Or call Crimestoppers anonymously on 0800 555 11.