Roberson was convicted of killing his 2-year-old daughter in a “shaken baby” case that many say led to an innocent man’s death sentence.

The Texas Supreme Court on Friday said the execution of a man convicted of murder in the 2002 death of his 2-year-old daughter could move forward, even as a state house committee seeks to subpoena the man for his testimony and its bipartisan members fight to spare his life.

The Texas Supreme Court on Friday cleared the way for 57-year-old Robert Roberson to become the first person in the U.S. to be executed for a "shaken baby syndrome" murder. A jury convicted Roberson of killing his 2-year-old daughter in 2002.