The seven-month-old child had been in Sydney Children’s Hospital at Randwick after being transferred from Wollongong Hospital in a critical condition last Wednesday.

As a result of the child’s death on Saturday, police on Wednesday formally laid a charge of murder against the boy’s father in Wollongong Local Court.

The 22-year-old man, who cannot be named for legal reasons, allegedly grabbed the boy around the waist and ‘‘vigorously’’ shook him after getting frustrated when the child would not drink his bottle about 9pm last Tuesday.

The boy was admitted to hospital the following day suffering chronic bleeding on the brain.

A CT scan revealed the child had bilateral subdural haematomas, requiring staff to drill holes into his skull to relieve the pressure.

Police allege family members living with the man and the child in a house at Warrawong witnessed the shaking incident, along with the man yelling at his son to ‘‘Shut the f--- up you little f---ing faggot’’.

However, the man denied any shaking had occurred when interviewed by police last Wednesday evening.

He allegedly told police he’d been playing video games that day in the bedroom he shared with the boy when the child let out a sudden high-pitched scream.

The man picked his son up, however the child’s limbs went stiff and he screamed a further five times, police documents tendered during previous court proceedings said.

He noticed the child gasping for air and he called triple-0, which directed him to begin CPR.

Ambulance officers arrived a short time later and found the boy in cardiac arrest.

He was immediately taken to hospital, where staff noted he was showing several signs associated with a brain injury.

During a later interview with police the man allegedly said the boy had been fine when he went to sleep on Tuesday evening but woke up the following morning crying and unsettled.

He said later that day the boy began to scream and became stiff.

The man, who has been remanded in custody over the incident, was supported in court on Wednesday by several family members.

The matter will be mentioned again in February.