The fire occurred in the first-floor flat of a two-storey residential property in Fairlisle Close, Clifton, at around 3.17am on Sunday.
Fire crews tackled the blaze, and it was extinguished at around 4am. A woman and two children, aged three and one, were treated at the scene for smoke inhalation.
They were taken to Queen’s Medical Centre in Nottingham.
Despite the efforts of medical staff, the two children were pronounced dead at the hospital.
The woman remains in a critical condition, police added.