Daniel Patrick Rodriguez appeared in court in an orange jumpsuit. He faces charges for murder and child endangerment.
The deadly encounter happened shortly after Byrd picked up his son from Commodore Sloat Elementary School last Wednesday.
Police say Rodriguez and Byrd got into a fight and Rodriguez stabbed Byrd to death as the victim's 8-year-old son watched.
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The boy's mother and grandmother attended the court hearing. Outside court the grandmother, Gloria Berry, said her grandson has not returned to school since the attack.
"I believe my grandson tried to render first aid. I don't talk to him about it. I try not to overly question him," said Gloria Berry.
The boy lives with his mother but Berry said Byrd would pick him up from school every day.
She said Byrd had been in a 20 year relationship with her daughter. She described him as a quiet person who did not get into trouble.
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Berry said passing by the school is painful for her, but she returned to drop off a thank you note for the person who grabbed her grandson and took him back to the school after the attack.
"This person brought my grandson back to the school and saved him," said Berry.
Rodriguez will return to court on Friday for arraignment. His lawyer wants him moved to a hospital for cancer treatment.
A parent's organization at Commodore Sloat Elementary School set up a GoFundMe for the victim's family which has raised nearly $79,000.