Parents who were deprived of time with their dying baby because of council failings have said no amount of money could make up for the hours lost.
Strict supervision orders were placed on Alan Hullah and Victoria Marshall when their son Thomas was made the subject of a safeguarding inquiry.
It meant Mr Hullah was turned away from seeing the four-month-old two days before he died in hospital.
York council, which later cleared them of any wrongdoing, has paid out £2,000.
Mr Hullah said: "No amount of money could ever compensate for the time we lost with our son."
He said it was horrific to be accused of hurting their "content and easygoing" baby and they had felt helpless.
"We also felt we were being judged by our reactions, that if we showed any signs of anger then this would lead to the council to believe we were capable of child abuse."
Forced out of home
Thomas, a twin to the couple's daughter Emily, was born on 3 November 2015 with a heart defect and Down's syndrome.
When he was taken to York District Hospital in early 2016 with breathing difficulties, a doctor noted injuries to his ribs, which the family insisted could have been caused by previous medical interventions.
Because of the injuries, social workers began a safeguarding investigation and the couple were not allowed any unsupervised access to Thomas or their other children Emily and George.
The couple were forced to move out of their family home and leave the other children with their grandparents.
When visiting Thomas in hospital, they had to be supervised at all times, either by relatives, friends or nursing staff, and were not allowed to stay with him overnight.
Access to seeing their son was restricted because the hospital said it was against their policy to supervise visits.
Despite the couple asking the council to provide a social worker, no-one ever came.
It was not until the final court hearing 11 weeks after Thomas died that the council withdrew orders in respect of their other children and said although Thomas's injuries were unexplained, they could not be attributed to his parents.
The whole handling of the case has been criticised by the Local Government and Social Care Ombudsman Michael King.
Mr Hullah said: "Thomas was so loved by our family... and will be remembered as such a beautiful and special little boy.
"We hope that we will eventually be able to remember him without also thinking about the appalling way we were treated by York council when he died."
The council said it "apologised unreservedly to the family" and fully accepted recommendations made by the ombudsman.