They are wanted for crimes including murder, rape, romance fraud and assault.
Their names and photographs have been released in the hope that members of the public may recognise them and report sightings.
Anyone with information on their whereabouts should call South Yorkshire Police on 101 or Crimestoppers on 0800 555111.
1. Murder
Ahmed Farrah is wanted over the murder of 21-year-old Kavan Brissett, who was stabbed in an attack in Upperthorpe in August 2018. Photo: Claire Lewis
2. Threats to kill
Keighran Michael Green is wanted by officers in Barnsley over criminal damage and threats to kill offences in the town. Keighran is believed to frequent the Goldthorpe and Thurnscoe areas of Barnsley. Photo: Claire Lewis
3. Fraud
John Eric Well, who is in his 60s and believed to also use the names Howard Walmsley and Howard Hemmings, is wanted in connection with romance frauds, during which three victims lost more than £400,000 between them. Photo: Claire Lewis
4. Rape
Vietnamese national Loi Le, aged 49, is wanted over the rape of a child in Tinsley, Sheffield, in 2012 or 2013. The victim, who is now 15, reported the matter in 2018. Le is also known as Tai Le and Cho Ngay Hanh Phuc. Photo: Claire Lewis