Dentrell Adam Claverie, 21, has been charged with murder.
Investigators said the shooting happened around 11:30 Sunday night at an apartment complex on Fondren near West Airport.
According to family members who spoke to Eyewitness News at the scene, Claverie was at the apartment with his two kids and his girlfriend when his father showed up.
Claverie and his father got into an argument and he shot him, police say.
The family claims that the father started attacking people and the shooting was in self-defense to protect Claverie's girlfriend, their 5-month-old twins and himself.
"His father was intoxicated, not speaking correctly. He caused the argument. He was putting his hands on me, my boyfriend, while I had my child in my hand. It was self defense. He had no reason to be on this property after we had already asked him to leave. We called the police. They took too long to come on the scene. He had to take matters into his own hands," said Claverie's girlfriend.
When officers arrived to the scene, they performed CPR, but the father died.