We were called to a large-scale disturbance on Elvaston Lane in Alvaston at 3.50pm on Sunday 20 August.
Four people were injured, and they were taken to hospital.
A scene remains in place in Alvaston and officers are in the area.
Four men aged 24, 28, 38 and 40 have been arrested on suspicion of possession of a firearm and violent disorder and remain in police custody.
Chief Superintendent Emma Aldred said: “We are keen to speak to anyone with information relating to the incident yesterday.
“We are aware of videos of the incident circulating online, we are carrying out investigations in relation to these and I would encourage anyone with footage to send it to us for enquiries to continue.
“Officers remain in the area to provide reassurance to the community, please speak to them if you have any information or contact us using the methods provided.”
Anyone who witnessed the incident, or has any information, is asked to contact us using any of the below methods, quoting the reference 739 of 20 August: