I am wondering, if there is an option to set up a special perimission for chosen users regarding the visibility on the given task in Jira , when this task contains sensitive data, like salary, bonuses?
You can setup an issue level security scheme. However, they work best when you can apply them to the whole project. It may be best if you can segregate all those type of issues into a separate project with limited access. for info setting up security schemes:
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