Hello @Deniss_Makarenkov
When you set candidate group for a specific task then by default UPDATE permission is granted for that task to all users who are members of that candidate group.
See below link for more details
You can use the filters concept to restrict the display of specific tasks to the assigned candidate group (see filter name “Tasks of a specific group” in below link)
https://docs.camunda.org/manual/7.7/webapps/tasklist/filters/#common-filters