The execution of Robert Roberson, an autistic Texas man convicted of killing his 2-year-old daughter, was halted at the last minute after a novel legal move by a bipartisan group of Texas House members who questioned the diagnosis of shaken baby syndrome that helped lead to his conviction.

The lawmakers effectively delayed the execution, which had been scheduled for Oct. 17, by issuing a subpoena for Mr. Roberson to testify before them on Monday. The move was highly unusual: The Texas Supreme Court said no precedent exists for how to address a legislative subpoena for a man who faces imminent execution, and it blocked it from going any further just before Mr. Roberson was set to die.

Mr. Roberson remains on death row while the courts consider how to handle the Legislature’s demand — though the judges said they would not be considering the larger question of whether his conviction should be set aside. Still, his supporters are hopeful that the postponement may afford time for a new consideration of the evidence.

In what is sure to be an extraordinary session, Mr. Roberson is scheduled to appear in person before a Texas House committee at noon Central time on Monday.

Who is Robert Roberson?

Mr. Roberson dropped out of high school and had some convictions for nonviolent crimes. He had a job delivering newspapers in the small town of Palestine, Texas, his lawyers said, when he got custody of his 2-year-old daughter, Nikki, in the fall of 2001.

A few months later, in January, his lawyers said, he was sleeping at home with Nikki when he woke up to find she had stopped breathing and was turning blue. She had been sick with a high fever, visiting doctors and the emergency room in the previous days, and had been prescribed medications including codeine and Phenergan. Earlier that night, she had fallen out of bed.