Anton Shields, of Hardwick Court, pleaded guilty to manslaughter at Derby Crown Court on Monday.
The 38-year-old was arrested on June 27 last year, initially charged with with assault occasioning grievous bodily harm with intent before this was changed to murder by the Crown Prosecution Service.
However, the plea of manslaughter was accepted a day before Shields’ trial was due to begin.
The baby was airlifted to hospital after paramedics were called to an address in Derbyshire where he was found to have serious head injuries.
He was taken to Sheffield Children’s Hospital but died two days later.