Residents were evacuated from Citadel Court after the alarm was raised at around 10pm on Monday night.
A team of 20 firefighters rushed to the scene of the blaze which started in a stairwell on the fifth floor of the 20-storey building.
Emergency services said that 6 people were treated for smoke inhalation.
It is understood that the fire was brought under control by midnight.
A fire service spokeswoman said: “An investigation into the cause of the fire is under way.”
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