The teenager, who is in Glasgow Royal Infirmary, is said to be “extremely distressed” after the assault, which happened in Wellhouse Road as snow swept across the the city.
Detectives have appealed for help to trace the suspects who were in a blue Peugeot 208 with distinctive yellow and blue wavy stripes.
The car, driven by a woman in her 20s with blonde dip-dyed hair, was first noticed by a woman as it drove up behind her vehicle at around 7.45pm.
Two men got out and tried to engage her in conversation but left after being ignored.
Shortly after, the same car was seen and its occupants threw an object at the vehicle of a 45-year-old man and his 16-year-old son.
When the father got out to speak to the two men he was threatened and chased off.
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His son was stabbed in the arm as the men, joined by a boy aged around 10 or 11, attempted to get into the car.
The suspects then returned to the Peugeot and made off over a grassy verge on to Langbar Crescent.
Detective Sergeant William Downie said: “There is no motive whatsoever for this outrageous behaviour and the people involved were clearly intent on causing injury, fear and alarm.
“Last night’s weather affected many people’s journeys home. There were several cars on Wellhouse Road, travelling slowly or even stationary at the time this dreadful incident occurred.
“I am urging the drivers, passengers who were in their cars at the time and have not already spoken to police to get in touch with us. You may have seen something which could prove significant.
“A family has been left badly shaken by what occurred and it’s imperative we trace the people responsible.”
The man who carried out the attack is described as white and of average build with short dark hair. He was wearing a tracksuit.
The second man is also white and in his early 20s and the third suspect is a young boy aged around 10 or 11.
Police also want to locate the blue Peugeot which has not yet been traced.
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