Anthony Walters appeared before Leeds Crown Court today over the incident at a house on Hill Top Mount, Harehills, on Wednesday January 24 this year.
Walters, of Beckett Road, Wheatley Park, Doncaster, spoke only to confirm his name, date of birth and nationality during the brief hearing.
Walters pleaded not guilty to each of the three charges of attempted murder.
He also pleads not guilty to a charge of arson with intent to endanger life on the same date.
A trial date was set for July 2.
Jonathan Sharp, prosecuting, said the trial is expected to last four days.
Walters was returned to custody after the hearing.
The victim did not initially realise how serious his injury was but reported the incident to police the following day.
The court heard he is expected to make an application for bail at a later date.
Firefighters had to rescue a mother and her two children through an upstairs window after a fire broke out in the early hours.
Police issued an appeal to trace a taxi driver who may have witnessed the incident.
A mother and her children, aged 14 and five, had to be rescued from the three-storey terraced property by firefighters.
They were treated in hospital for the effects of smoke inhalation.
Specialist fire investigations later confirmed the fire had started in the hallway through the letterbox and the trio had to flee to the upstairs of the house for refuge as they could not get out.
After the incident Det Insp Dave McDougal, of Leeds District CID, said: “The fire quickly spread through the downstairs of the house and to the stairwell leaving the victims no option but to seek refuge in the attic where they were rescued by firefighters.
“If it hadn’t been for the courageous actions of the fire service, this incident could easily have had very tragic consequences.
“We are treating this incident very seriously and are carrying out extensive enquiries, including checks on CCTV in the area.