The incident happened on the Erganagh Road in Omagh.
Chief Inspector Clive Beatty said: “Police attended the scene at approximately 10.45pm.
“The man had sustained serious head injuries and was receiving treatment from ambulance staff at the scene before being taken to hospital.
“The man remains in a critical condition in hospital.
“I am continuing to appeal to anyone who may have witnessed any suspicious activity in the area at the time, particularly regarding the movements of two Quad motorbikes to contact officers in Omagh Police Station on 101, quoting reference 1438 of 07/07/17.
“Or, alternatively if someone would prefer to provide information without giving their details they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.”