The incident occurred at around 2.40pm on Sunday (16/10) on Churchill Avenue, where the four men, who are believed to be known to each other, were seen fighting in the street with weapons.
A black Audi A3, a red Vauxhall Astra and an orange dirt bike are believed to be associated with the incident.
A 34-year-old man from Aylesbury has been arrested on suspicion of violent disorder and remains in police custody, but officers are still looking for information.
Investigating officer, PC Jemma Millward-Samuel, based at Aylesbury police station, said: “I would like to appeal to anybody who may have been in the area during the time of this incident, witnessed anything or has information, to please get in touch.
“I’d also ask anyone who may have dash-cam or doorbell footage from the local area to please check it, in case it has captured something that could help the investigation.
“You can get in touch by either making a report online or by calling 101 quoting reference number 43220465377.
“Alternatively, for 100% anonymity, you can also call the independent charity Crimestoppers on 0800 555 111.”
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