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Following a six-week trial at Birmingham Crown Court, Zidann Edwards and Diago Anderson, both 20, and a 17-year-old - who the law says cannot be named because he is under 18 - were all charged with attempted murder.
The 17-year-old was also charged with having a firearm with the intent to endanger life and having a prohibited weapon.
They were found guilty yesterday (2 August) and will be sentenced on October 7.
The shooting occurred in the Hockley Circus underpass in Birmingham in November of last year. The boy and his friends were in town and on their way to get some food when he was attacked.
Despite his injuries, the boy was able to call 999 and inform the ambulance service that he had been injured.
Before paramedics arrived, firearm officers were the first on the scene and provided life-saving first aid.
Detectives discovered CCTV footage of a car driving down the A41 before abruptly stopping in a service road. Edwards, Anderson, and the 17-year-old all escaped.
The 13-year-old boy and his friends were then chased into the underpass, where he was shot in the back and paralysed by a home-made shotgun known as a slam gun.
The video showed Edwards, Anderson, and the 17-year-old boy fleeing the scene and driving away. Police later tracked down and recovered the car they were in, and forensic experts were able to link the trio to the vehicle.
Officers also discovered a handgun and a slam gun at an address associated with the 17-year-old, and further investigation revealed that this was the weapon used in the incident.
"The unprovoked and callous actions of Zidann Edwards, Diago Anderson, and the 17-year-old boy changed the life of an innocent 13-year-old boy and his family forever," said Detective Inspector Michelle Cordell of Force CID.
The consequences of their actions are heartbreaking, and my thoughts are with the boy, his family, and friends."
My team worked tirelessly from the start with internal and external colleagues and partners to gather and present the evidence in this case. Their combined efforts and dedication have resulted in justice for the victim and his family.
"Our primary goal is to prevent these incidents from occurring, but unfortunately, we continue to see gun violence on our streets." We need our communities to band together to help us combat gun and gang-related crime."