Charlie Gard's parents have told a judge reviewing the benefits of allowing the terminally-ill baby to undergo a treatment trial abroad that they feel "stripped of their rights".
Chris Gard and Connie Yates want Mr Justice Francis to rule that 11-month-old Charlie, who suffers from a rare genetic condition and has brain damage, should be allowed to undergo a therapy trial in the United States.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, say the therapy is experimental and will not help.
They say life-support treatment should stop.
The couple, who are in their 30s and come from Bedfont, west London, are mounting the latest stage of their fight at a hearing in the Family Division of the High Court.
Charlie's parents have already lost battles in the High Court, Court of Appeal and Supreme Court in London.
They have also failed to persuade European Court of Human Rights judges to intervene.
The couple say there is new evidence and want Mr Justice Francis to carry out a fresh analysis of their case.
Mr Justice Francis is analysing evidence at a hearing in the Family Division of the High Court in London.
A lawyer representing Great Ormond Street bosses told Mr Justice Francis they do not believe there is any role for a court.
"Charlie's parents fundamentally believe that they alone have the right to decide what treatment Charlie has and does not have," said Katie Gollop QC in a written statement.
"They do not believe that there is any role for a judge or a court.
"They feel they have been stripped of their rights as parents."
But Ms Gollop said Great Ormond Street is bound by "different principles".
She said children also have rights and the hospital mission statement is: "The child first and always."
Ms Gollop said doctors treat children as individuals and act in a child's best interests.