The 22-year-old man was in his BMW car on Back Maud Avenue, at the junction with Maud Place, when a black Volkswagen Passat pulled up on Saturday afternoon.
A shotgun was then fired at the BMW, damaging the bonnet and windscreen.
The victim, who was not injured, repeatedly rammed the Passat and drove off from the scene.
The Passat was later found burnt out in Cardinal Square.
On that occasion, two men received minor injuries when a shotgun was fired at a car.
Detective Chief Inspector Jaz Khan, of West Yorkshire Police’s Firearms Prevent Team, said: “Both of these incidents could have had far more serious consequences and are being treated as attempted murders. We believe these have been targeted attacks linked to an ongoing dispute."
Six men have now been arrested on suspicion of attempted murder in relation the shooting on Saturday.
One man was arrested in Leeds city centre by armed officers this afternoon and another man was arrested in an armed operation at an address in Whinmoor in the early hours of this morning.
Four further men were arrested this afternoon when armed officers stopped a vehicle in Bradford.
Det Chief Insp Khan said: "We have a team of specialist detectives, supported by firearms officers, who are continuing to carry out enquiries into these incidents and our investigations are progressing positively with the arrests we have seen today.
“We would however still like to hear from anyone with any information that could assist the investigation, particularly if they have any knowledge of the wider circumstances surrounding these incidents. We would remind people that the independent charity Crimestoppers can be used as a secure and anonymous way of passing on information.
“The criminal use of firearms on our streets is something we will always treat very seriously and we will do everything we can to identify those responsible and will also take appropriate action to prevent any further incidents."
Officers from the local neighbourhood team will be carrying out extra patrols of the area to reassure the community and distributing leaflets to homes in the area to encourage people to share information with police.
Anyone with any information is asked to contact police via 101, quoting crime number 13170501767.
Alternatively, call the independent charity Crimestoppers anonymously on 0800 555 111.