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In a stunning chain of events, a man scheduled for execution was granted an eleventh-hour reprieve by the top court in Texas. But he is not yet out of the woods.

Robert Roberson, 57, was due to be the first American ever put to death over murder charges related to what is known as "shaken baby syndrome".

Set to die by lethal injection 17 October, he was spared - for now - by Texas lawmakers and the state Supreme Court.

What happens next could lead either to a re-scheduled execution or an ultra-rare act of clemency in the state that leads the way for capital punishment in the US.

Roberson - who was convicted in the death of his two-year-old daughter, Nikki Curtis - was hoping to be shown leniency, though he lost multiple appeals in state courts.

On Wednesday, the state's parole board rejected Roberson's bid for clemency, recommending against commuting his sentence to life in prison and against delaying his execution.

Texas Governor Greg Abbott, who has the power to halt an execution regardless of the board's recommendation, also declined to do so. In nearly a decade as the state's chief executive, Abbott has commuted a sentence only once.

But the same day, in response to calls to spare Roberson's life, a bipartisan group of lawmakers in the Texas House of Representatives issued a subpoena for him to testify before their panel next week.

The purpose of the panel is to address questions about Roberson's case, including new scientific developments that have called key details surrounding his conviction into question, according to CBS, the ������̳'s US news partner.

Some 90 minutes before Roberson’s scheduled execution last week, the House criminal jurisprudence committee secured a temporary restraining order against the state, forcing it to hit pause on the procedure.

Although a divided Texas Court of Criminal Appeals struck down the order, the lawmakers appealed to the Texas Supreme Court, which swiftly halted the execution so Roberson could sit before the House panel Monday.

But he did not appear in person at the state capitol in Austin as expected, after the state's attorney general refused to allow it for security reasons.

The legislature also refused to have Roberson appear virtually because he has autism and he is not familiar with modern technology after spending 20-plus years in prison.

Instead of hearing from the convict on Monday, the five Republicans and four Democrats on the committee heard from experts, including Phil McGraw, the television host known as Dr Phil. Mr McGraw spoke about how the state's junk science law, which lets inmates challenge convictions based on later discredited science, might have affected his case.

He said Roberson did not have due process or a "fair trial".

"There's no such thing as shaken baby syndrome," Mr McGraw said, noting there would be "very clear signs" of abuse "that were not present in this case".

Roberson has long maintained his innocence and his attorneys say his daughter was suffering from multiple health issues before her death, including side effects from prescribed medications inappropriate for a toddler and acute pneumonia that had progressed to sepsis.

Advocates have also said that manifestation of Roberson's autism, which went undiagnosed until 2018, were used against him during the criminal inquiry.

Brian Wharton, the lead detective on the case, is among those supporting a plea for clemency, writing in a letter that he "will be forever haunted by my participation in [Roberson's] arrest and prosecution. He is an innocent man”.

But prosecutors maintain Roberson is guilty of murder and that there is evidence Nikki Curtis was shaken and had suffered abuse at the hands of her father.

"Everything that he continues to complain of has been litigated in state and federal court, and every court has rejected his arguments," they wrote earlier this month.

According to data compiled by the Death Penalty Information Center (DPIC), Texas has executed 591 people since the US Supreme Court reinstated the death penalty in 1976.

That is more than one-third of the 1,602 executions carried out across the country.

During that same time period, the state has granted clemency on only three occasions, DPIC figures indicate.