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The event began at 10 a.m. and will go until 4 p.m. at 4130 1/2 Cavalcade St.
Plates of barbecue will be sold at $10 each, but volunteers will also be accepting other monetary donations.
Lajah Richardson, Garrett's fiancée, has also set up the following GoFundMe page to raise money for Garrett's recovery and medical expenses.
SEE RELATED STORY: 'They called each other brothers': Fiancée of critically injured Pct. 4 deputy speaks
Garrett was shot in the back multiple times and had undergone surgery last Sunday. Richardson said she did not immediately tell Garrett that his best friend, Deputy Kareem Atkins, was killed in the shooting because she did not want the terrible news to jeopardize his recovery.
Another deputy, Juqaim Barthen, was also wounded in the shooting. He has since been released from the hospital.
The search continues for the shooter, and the reward to find the person who police say ambushed the three constable deputies is now at $75,000.
The amount includes $10,000 offered by Crime Stoppers of Houston, $40,000 from billionaire Tilman Fertitta, who chairs the Houston Police Foundation, and $25,000 donated anonymously.
The 100 Club of Houston also disclosed donating $20,000 to Atkins' widow and two small children.
MORE: Harris Co. Precinct 4 constable deputy released from hospital as reward increases to $75,000