Jared Balogun is accused of fatally shooting Messiah Justice Marshall on June 14 at the Nob Hill Apartments.
The baby boy's 22-year-old father told police he was outside with Messiah in his arms when three men approached him shooting. They continued even as he ran away with his baby in his arms, he said.
Balogun is charged with capital murder.
The family set up a GoFundMe account to help cover funeral costs.
In an emotional interview with Eyewitness News, Aliyah Scott said her son loved Paw Patrol and Bruno Mars' songs, and always drew people's attention.
FULL VIDEO: Boy of mother shot, killed talks about how special he was
"He was something special. He was so advanced. He learned fast. He picked up fast," said Scott as she wiped away tears. "He showed me the true meaning of unconditional love."
Scott said she was inside her apartment when the shooting happened.
"I was about to take a nap. His dad had him. They were going outside to take the trash," said Scott. "They were loud. It was like an echo. It was really close."
"I just want that person to turn himself in. Do what you got to do. You know what you did wrong. No need to hide it. You're going to get God either way," said Scott. "Please, just please go to the police or someone. Let them know what was happening."
A neighbor was watching her newborn daughter as she raced to find Messiah.
The father ran to a nearby Valero gas station for help. A woman recorded the frantic moments as the father cradled his dying son in his arms.
"He was screaming and said, 'Somebody shot my baby,'" eyewitness Mari Hidalgo said.
"I ran to the Valero. They said there was a baby at Valero. I ran to Valero," said Scott. "His dad ran up to me saying, 'It was Messiah. It was Messiah.' All I could say was, 'What happened to my baby? What happened to my baby?'"
On Thursday evening, Houston Police Chief Art Acevedo spent about an hour at the apartment complex before addressing residents' safety concerns in a meeting closed to the media. Marked police units and gang and bike patrol officers were visibly present all day.
VIDEO: A closer look at the death of Messiah Marshall
"They're extremely dangerous. Obviously they're armed and have no conscience," said Chief Acevedo.
"Callous" and "cowardly." Those are words Acevedo used to describe the suspects involved in the fatal shooting of 10-month-old Messiah Marshall.
"His journey was cut short by cowards that have absolutely no respect for the sanctity of life. They crossed a line. You don't shoot at a man holding his 10-month-old son," Acevedo said.
Houston police arrived on the scene in the 5300 block of North Braeswood just after 1:30 p.m. June 14.
"That baby smiled every time you looked at him, every time you looked at him. He was just the sweetest baby you want to see. You take an innocent life...it's cowardly," said Willie Mason, the boy's grandfather.
The father told police he did not know the gunmen, but Acevedo said there are witnesses at the apartments who he hopes will come forward with information.
"One, he didn't have a shirt on. He had gym shorts. Looked like he had braids or something, dreads. The other one had on a red hat, maybe a red shirt," neighbor Malik Collins said.
Police said the neighbor is spot on with the description.