A Chesterfield man arrested on suspicion of terrorism offences earlier this week has been named in the national media as Hazhar Star.
Also known as Andy, the 31-year-old is believed to be the owner of the Mermaid Traditional Fish Bar on Sheffield Road, which has been cordoned off by police since the arrest on Tuesday.
Three arrests were also made in Sheffield for similar alleged offences as part of an investigation by the North East Counter Terrorism Unit.
The four men were taken to a police station in West Yorkshire and detectives from the counter terrorism team have been given until 4pm on December 25 to charge, release or apply for a further extension to custody.
On Tuesday, a part of Sheffield Road and King Street North in Whittington Moor were cordoned off while searches took place.
An Army bomb disposal team were also at the scene on Tuesday and Wednesday.
There is still a police presence outside the Mermaid fish and chip shop today.