The issue began in April 2017 in Providence, Rhodes Island, where he lived, when police officers found his son in a dying condition, bleeding from the mouth and nose.
The United States has declared Olalekan Olawusi, a Nigerian man, wanted and placed a $25,000 bounty on his head.
In a public notice on Monday, the US Supervisory Deputy Marshal, Don Freeman, offered $25,000 to anyone with information that could lead to the arrest of the suspect.
Mr Olawusi, who is currently on the run, was arrested in the US over charges of first-degree murder and two counts of inflicting serious bodily injuries to a child.
The issue began in April 2017 in Providence, Rhodes Island, where he lived, when police officers found his son in a dying condition, bleeding from the mouth and nose.
The infant with cardiac arrest was rushed to a hospital for immediate medical attention.
A hospital assessment showed that the child had at least 18 injuries across its body.
The examination showed a fracture in the skull, subdural hematoma, significant brain injury, and fractures to the ribs, clavicle, legs, and arms of the unnamed child.
In a bid to resuscitate the child, he was placed on life support in the hospital but died after six months from the incident.
The arrest
Days after the discovery, the police operatives apprehended and charged Mr Olawusi on 20 April 2017 with first-degree child abuse.
But he was released the same day and subsequently fled.
When the baby died on 31 October 2017, the prosecution team added a murder charge to the case.
Since then, the police have been on the lookout for the fugitive, even requesting the support of the US Marshals Service (USMS) to find him.
Investigation shows that Mr Olawusi flew out of John F. Kennedy International Airport in New York on 20 June 2017, months before the child's death, using his Nigerian passport.
Wanted
The US government believes Mr Olawusi might have been helped to escape by his friends and family members in Nigeria, saying that could pose serious danger to other innocent children.
"Mr Olawusi is wanted for the abuse and murder of an innocent child, and has fled the country to avoid justice.
"We have placed Mr Olawusi on our 15 Most Wanted list due to the heinous crimes he's committed and the threat he continues to pose to the public," Director Ronald L. Davis of the US Marshals Service said.
He noted that the US government would use all available resources to find him and bring him to justice.
The US Marshals said Mr Olawusi, stands 5 feet 8 inches tall and weighs approximately 185 pounds. He has black hair and brown eyes.