"Jones stated that he believed the children were going to kill him, chop him up, and feed him to the dogs", the arrest warrant said.
A United States jury has sentenced a man to death after convicting him of murdering his five young children in 2014 before driving their decomposing bodies through several states and dumping them in Alabama.
Jones said in a 2014 phone call from prison played in court that he "snapped" when he killed Nahtahn, six, because the child was crying for his mother.
Solicitor Rick Hubbard told a jury Thursday that 37-year-old Timothy Jones Jr. deserves to be executed instead of getting life in prison, which Hubbard said would be like sending "Timmy to his room".
Jones has been sentenced to death after being found guilty on five counts of murder in the deaths of his children. "Nothing justifies what you've done", she told Jones.
Jones admitted he exercised six-year-old Nathan until he collapsed and died, then several hours later chose to kill the other four children.
Mr Hubbard said Jones was a selfish, evil man who abused his children and murdered them out of rage and fear of being caught. "He sentenced his kids to death", Mr Hubbard said.
He is just the second person to be sent to South Carolina's death row in five years.
He confessed to the slayings, telling investigators that he first forced his 6-year-old son Nahtahn to exercise until the point he collapsed and died before strangling and choking the boy's siblings - Merah, Elias, Gabriel and Abigail. He then used a belt to choke 2-year-old Gabriel and 1-year-old Abigail because he said his hands were too big.
He strangled the other four, before driving aimlessly around for nine days with the bodies in his auto, dumping the remains in black bin bags in rural Alabama.
He was arrested hours later after an officer at a traffic checkpoint in Smith County, Mississippi, said he smelled a disgusting odour of decomposition.
The state has not executed anyone since 2011 because it lacks the drugs to carry out lethal injection. Prosecutors entered photos showing what was inside the bags into evidence, but didn't show them to the jury. Attorney says Jones' mom has been institutionalized for 20 years with diagnosed schizophrenia.
Defense attorney Casey Secor asked jurors to punish Jones severely with life without parole, but show compassion for his family so they don't endure any more death.
Jones' defense team argued that he should receive a sentence of life without parole, with the support of the children's mother. How many more funerals does this family have to go to?
Mr Hubbard began his closing argument by asking if the jurors had ever heard of a crime more horrendous than what they have listened to over four weeks of testimony. "How much more heartache to they have to endure?"