Liam Whoriskey, of Glenabbey Gardens in the city, was found guilty in October of the manslaughter of Kayden McGuinness.
The toddler was found dead in his family flat in Derry in September 2017.
Peter Irvine QC said the case’s aggravating factors meant a life sentence was an option.
He was speaking at a sentencing hearing at Londonderry Crown Court on Friday.
The Public Prosecution Service barrister said Kayden’s age, vulnerability and that he was being assessed as autistic were among the case’s aggravating factors.
He said that Whoriskey had sole custody of Kayden on the night he was killed and it should be taken into consideration that it had not been an isolated, violent attack.
“The PPS believes this is a truly exceptional case because of the aggravating features and because there is no mitigation present,” said Mr Irvine.
“Accordingly it is our respectful submission that this court is entitled to reflect the gravity of this case by considering a starting point beyond the normal sentencing range.”
Mr Irvine said he was also applying for a Violent Offences Prevention Order to be imposed on Whoriskey.
Defence barrister Mr Mallon told the court he rejected the prosecution’s claim that it was a truly exceptional case.
He said it was an unusual, tragic case and accepted the verdicts of the jury.
Mr Mallon said the collective evidence from several medical experts was that the injuries inflicted on Kayden were of a minor, mild or moderate nature.
The barrister also questioned the Probation Board’s assessment that Whoriskey was dangerous.He said that assessment was not supported in terms of a previous criminal record for similar offences.
“Any offence involving the death of a child is a very serious offence but, in this case, there is no evidence of intent and I would urge the court to claw back from the Probation Board’s assessment of dangerous,” he said.
Mr Mallon said he also rejected the prosecution’s claim that the case lacked mitigating factors.
He said Whoriskey had financially supported Erin McLaughlin and her two children at a time when she was struggling financially, he had attended the birth of her second child.
Whoriskey treated the two children as if they were his own and had become engaged to Kayden’s mother the week before the child was killed, the defence barrister said.
Judge Philip Babington said it was a difficult case which required some consideration.
Whoriskey was remanded in custody to be sentenced on Monday, December 16.