Dear candidate, yes it's true that M.Phil Degree holders are exempted from appearing for the entrance exam for PhD in Calicut University.
Also those candidates who are exempted from the entrance test can seek admission any time during the academic year.
You can check this official website link for more information (https://www.google.com/url?sa=t&source=web&rct=j&url=http%3A%2F%2Fwww.cuonline.ac.in%2F&ved=2ahUKEwisuIeVx8blAhVFb30KHcRODEoQFjAFegQIBhAB&usg=AOvVaw0ad23lcbhFYdht9orTHdtx&cshid=1572527176578)
All the best
Hope this helps