A Texas prisoner who is facing execution having been sent to death row on the basis of “shaken baby syndrome”, a child abuse theory that has been widely debunked as junk science, has had his petition to the US supreme court denied.

The country’s highest court issued its denial on Monday morning giving no explanation. Robert Roberson, 56, who was sent to death row in 2003 for shaking his two-year-old daughter Nikki to death, had appealed to the justices to take another look at his case focusing on the largely discredited forensic science on which his conviction was secured.

The court’s decision leaves Roberson’s life in jeopardy. Having come within four days of execution in 2016, he has already exhausted appeals through Texas state courts and must now rely on the mercy of the Republican governor Greg Abbott who rarely grants clemency.

“Robert Roberson is an innocent father who has languished on Texas’s death row for 20 years for a crime that never occurred and a conviction based on outdated and now refuted science,” the prisoner’s lawyer, Gretchen Sween, said.