Sean Hackett,18, admitted to police he shot his father at their family home near Augher - and that he suffered from depression.
As police brought the defendant to court, cameramen were pushed and shoved by some of his friends.
His mother, sister and two brothers were in the public gallery as he was charged with killing his 60-year-old father, Aloysius.
The father-of-four's body was found in the back yard of his family home on the Aghindarragh Road on Friday night.
Sean Hackett was present when emergency services arrived at the scene of the shooting.
At first, he said he had found his father after returning from a night out, but later requested to speak to the police again.
A detective confirmed to Omagh Magistrates' Court that Sean Hackett initially denied involvement in the death of his father, but later admitted: "I did it, I shot him".
After his confession, Sean Hackett remained silent for three subsequent days of questioning, the detective said.
He, instead, submitted a written statement to police in which he admitted involvement in an "incident" which resulted in the death of his father, a man he "loved very much", the officer said.
He also informed police that he has depression, she said.
A defence lawyer told judge Bernie Kelly that the young man still had the full support and love of his mother Eilish, sister Aileen and two brothers Kevin and Conor.
The young sportsman captained last season's Tyrone minor Gaelic football team. His mother wept on a number of occasions in the public gallery. At one stage, she and her children exchanged waves with the defendant in the dock.
This is a tragic case and no-one can possibly contemplate what the family has gone through and will go through.
Mr Justice Horner
Police have been unable to establish a motive, the detective said.
"We aren't aware of why this happened," she said.
The court heard that he texted a friend asking for a gun on two occasions, the latest on New Year's Day. When he was arrested, two spent cartridges were found in his pocket.
Forensic tests have since been carried out on the shotgun. "Police believe that was the weapon used," the detective told the court.
The detective objected to granting bail on the grounds that the accused may interfere with potential witnesses, could flee the jurisdiction or could commit further offences.
She also raised concerns about the accused's health and said he might need immediate treatment.
"He may be both a significant risk to both himself and others."
Applying for bail, Hackett's lawyer Mr O'Kane said it was a "tragic incident for everyone involved".
"He enjoys the full love of his family. His mother, his sister and two brothers are in court today," he stressed.
"It is the family wish that Sean would be released to attend his father's funeral tomorrow."
A psychiatrist is on stand-by to assess his client's condition, Mr O'Kane said.
Sean Hackett's bail application was rejected, but he was granted a few hours of compassionate leave to attend his father's funeral in Augher on Wednesday.
He will be accompanied at all times by two people - his lawyer, Adrian O'Kane, and Tyrone Gaelic football manager Mickey Harte and will not be allowed to speak to anyone else, including family members.
In the High Court on Tuesday afternoon, Mr Justice Horner rejected a prosecution appeal that he should not be given four hours compassionate leave.
During the hearing, the Judge was told that the teenager had allegedly also tried to strangle his mother months earlier.
Meanwhile, a 17-year-old boy arrested on Sunday by detectives investigating the crime has been released pending a report to prosecutors.