Yela allegedly murdered his twins, a girl and a boy, while exercising his visitation rights while on holiday from Spain.
In a brief appearance in the Wynberg Magistrate's Court on Wednesday, defense lawyer William Booth argued that Yela needed immediate medical attention.
He had reportedly suffered a wound to his abdomen before his arrest and had been treated at Victoria Hospital in Cape Town.
Last Wednesday, Yela was remanded to Pollsmoor prison to await a bail hearing after Booth's request to have him remanded to hospital under police guard was denied.
This week, Magistrate Goolam Bawa again denied the request and remanded Yela to Pollsmoor until April 25 for the next court appearance.
On April 6, Yela was arrested after fleeing his Princess Beach holiday apartment in Hout Bay after the twins' mother discovered their bodies.
Last week, the court heard that Yela had contacted the mother, Julia Engelhorn, via a text message to invite her for lunch.
State prosecutor Benito Adonis alleged Yela then told her he had killed their twins.
The couple divorced in 2015.
Their three children, the twins and a seven-year-old son, had previously visited Yela in Spain during the December/January school holidays.
On the morning of the murders, it's believed Yela had dropped the seven year old at school.
After the mother discovered the bodies of the twins, Yela allegedly fled in Engelhorn's car.
He was later arrested in Wynberg.
Yela was due to return to Spain that night.