The incident, which is understood to be football related, happened at Drumchapel Station.
Police say that a fight broke out on the Glasgow Central to Drumchapel train. When the train stopped at Drumchapel Station, the brawl continued on the platform.
A 34-year-old man was struck and fell to the ground before falling
onto the track and sustaining a leg injury.
He was taken to the Western General hospital where he was released after treatment. Another man, 18, who was with him, was uninjured.
British Transport Police are looking for four men in their late teens to early 20s with short dark hair.
They made off in the direction of Garscadden Road through the car park after the incident at 2.36pm on Saturday.
British Transport Police can be contacted on 0800 405040.