Joshua Martin, now 20, of Salisbury Close, Alton, was cleared of murder but found guilty of manslaughter following his April trial at Winchester Crown Court.
With the seven years custody to be served in a young offenders’ institution, Martin was sentenced to serve a further five years on licence.
He was warned by the Hon Justice May that if he committed any offence while on licence he would go back to jail.
She told him that any contact he was to have with young children in the future “is to be closely monitored”.
A charge of murder, to which Martin had pleaded not guilty at the start of the trial, was reduced to manslaughter.
On Friday Martin’s parents were in the public gallery and Ezmai’s mother Jemma Pethybridge, who was 19 at the time Ezmai was killed, was also in the court. She began sobbing loudly as Martin was sentenced and was helped by two friends as she left.
In a statement read in the court she said she felt her life had been taken away because her daughter’s life had been taken away.
It was on June 28, 2015, in the flat she shared with Martin, then 18 - in New Road, Bordon and “described as having a pressure-cooker atmosphere” - that Ms Pethybridge returned from having a shower to find Ezmai lying on the floor, not breathing, appearing lifeless with “milky vomit” coming from her nose and mouth.
During a 999 call, which was played at the trial, Martin was advised to administer chest compressions while the couple waited for the ambulance to arrive.
Ezmai was taken to the Royal Surrey County Hospital, in Guildford, before being transferred to St George’s Hospital, in Tooting, London, where she later died.
She had received a head injury which had caused a subdural haemorrhage and severe brain damage, the court heard. She also had bloodshot eyes, said to be “consistent with being shaken”, and had eight bruised or fractured ribs, which were not damaged by the chest compressions.
Ms Pethybridge went with her daughter in the ambulance while Martin stayed behind and, in a rage, “trashed the flat”.
Before the sentencing of Martin, prosecutor William Mousley QC had told the court that since the trial the defendant, after one day in remand, had been placed under curfew.
He read a statement made by Ms Pethybridge in February last year about the effect the death of her daughter had had on her.
“What happened in 2015 I will try to describe,” she had said. “I feel disgusted, annoyed and mentally not completely right.
“I get frightened leaving the house and since Ezmai died I have had great difficulty in showering.”
She also said she did not trust people and had difficulty remembering that part of her life.
“I feel my life has been taken away because my daughter’s life was taken away,” she said.
Defending, Richard Barraclough QC said his client had been “stressed at the time” when he showed this disproportionate force of violence towards his daughter.
“He was very young at the time, 18 years of age, and immature and was also struggling as he had taken his responsibilities to his baby daughter seriously,” Mr Barraclough told the court.
“He was working long hours as a labourer under pressure to support the family and this descended into this patten of violence.
“But what can I say that will reverse the terrible loss of this baby?”
Justice May told Martin: “Your baby daughter was six weeks old and in your care when she suffered a fatal attack consistent with being shaken and her head hitting something hard.
“But you have not given an account of what happened - just she was lying on the floor while you Hoover around, and you saw milky vomit coming from her mouth.
“When she was taken to hospital you stayed behind and pulled down the curtains in the flat and smashed furniture.”
From the reports, said the judge, the relationship the defendant had with Ms Pethybridge “had been demanding” but “you seemed to be doing well, and you supported them, and your parents were proud of how you were doing”.
“However, things weren’t going well and the defendant didn’t want to stay but only stayed because of his daughter so the flat had become a pressure cooker.”
On that day in June, the judge told Martin: “You had been playing on your Xbox all day and you stopped and attacked Ezmai.
“Your temper against your daughter was instant and this rage against your daughter is of great concern and there has been no acknowledgement by you of how Ezmai got these injuries. So I have taken into consideration that any contact you have with young children in the future is well monitored. The fact is you caused her death, although you have not revealed how she received these fractures, and your rage was just short of murder.”
Martin made no response as his sentence was passed and just turned and left the dock.