The child, who came to be known as Baby Peter, was found on the doorstep of the vicarage of St Peter’s Church, in Hough Lane, Bramley, on November 23, 2016.
Detectives say they have exhausted all lines of inquiry in their efforts to trace the infant's mother, but still hope she will come forward so they can check on her and make sure she has the support she needs.
Baby Peter, who was white, was found inside a Tesco Bag for Life and had been wrapped in a distinctive blue striped towel and a men’s white 15-inch collar shirt from clothing firm Dunnes.
It was quickly established that he had reached full term and the placenta was still attached, so in all likelihood he had been left at the church soon after he was born.
It remains a mystery whether it was the mother herself or someone else who left the baby on the steps of the vicarage, which is not easily identifiable to those unfamiliar with the area.
The infant appeared lifeless and was cold to the touch but was given CPR at the scene by paramedics before being taken to hospital, where he was pronounced dead.
The tragic events prompted an outpouring of tributes from the local community, with flowers, teddy bears and notes left outside the church as news of the baby’s death became more widely known.
The Rev Paul Crabb, who found Baby Peter, led prayers for the child and his mother and, a year on, reached out to the mother in an emotional message, saying the people of Bramley "have not forgotten your baby or you".
West Yorkshire Police has previously set out the efforts it had made to trace the boy's mother before concluding that it had exhausted all lines of inquiry.
The force said officers carried out extensive enquiries over the last few years including contacting schools, health visitors and midwife services.
Media appeals were made - including a video appeal on the first anniversary of Baby Peter's death - and a mass leafleting and poster campaign was conducted in the area.
Detectives also trawled CCTV around the vicarage and wider area and viewed several hours of footage.
A DNA profile for the mother was recovered but is not recorded on the police database. The DNA found on the shirt suggested it had been worn by a female, the force said.
Detective Superintendent Nicola Bryar, who led the investigation, said last year: “Sadly we have now explored and exhausted all the available lines of enquiry without being able to identify the mother of this baby boy.
“Throughout this investigation, her welfare has remained our main concern. The immediate concerns we had for her health have lessened with the passage of time but we are still keen to trace her and make sure she has the help and support she needs after what has clearly been a traumatic experience.
“On the first anniversary of her son being found I released a special video message to appeal directly to her to contact me.
“The sentiments I expressed in that message a year ago remain exactly the same today. She is not in any trouble with the police and there is still an opportunity for her to come forward."