Nottinghamshire Police said the two children were pronounced dead at the hospital, while the woman remains in critical condition.
On Sunday evening a man from Clifton was arrested on suspicion of murder and attempted murder, detectives stated. He remained in custody overnight for questioning.
The Detective Chief Inspector leading the police tea, Greg McGill, said "This is a deeply tragic incident and we have a large team working tirelessly to understand the full circumstances."
Further comment was added, "whilst we have now made an arrest, the investigation remains at an early stage and we are continuing to appeal to anyone who has even the slightest bit of information or even CCTV or dash – cam footage, to please come forward."
Neighbouring buildings were evacuated during the incident. The fire was extinguished at around 4am.
A local resident was alerted by a fire engine's lights while watching a movie, and then saw smoke billowing from the rear windows of the first – floor flat.
He said the older child was brought out of the property first, with the one year old being carried out by a firefighter shortly after. "It's sickening. I feel so sorry for the family."
He also stated, "How is she going to feel when she finds out she's lost the children?"
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