The incident happened Monday afternoon on the 200 block of Market Street, not far from Fourth of July festivities held in the city.
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Police say a 20-year-old male was shot once in the abdomen and once in the right leg.
He was transported by medics to Jefferson Center City, where he has listed in critical but stable condition.
Officials say the incident began as a verbal altercation between people in two vehicles that ended at the intersection of 2nd Street.
According to police, the driver of one of the vehicles threw a drink at another car. That led to bottles being thrown back and forth between the vehicles.
When two men got out of their vehicle, police say the man who threw the first drink opened fire.
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Police were reportedly in the immediate area when the shooting took place.
Officers were then able to quickly apprehend the two men involved, pending investigation.
A weapon was also recovered from the scene.
Police say two individuals had permits to carry.