Summary

The user should be allowed to view only the tickets assigned to them in Company-managed projects and the tickets assigned to other users should not be visible. 

Environment

Jira Cloud.

Solution

You can achieve this requirement by using the project permission scheme. You need to grant Browse Projects permission to the Current assignee.

1. Go to Project → Project settings → Permissions
2. Click Actions -> Edit permission
3. Next to the  Browse Projects permission click Update
4. Select Current Assignee and click Update.

Note:

1. You need to remove all the unwanted project roles, groups, and users from the Browse Projects permission in the permission scheme used by the project for this change to be effective.
2. When the Current Assignee is given the Browse Project Permission, all the users are able to view this Project. However, they can't view issues or create issues, but they can see the project from the View All Projects page.
3. All the users will also be able to see the project name at the project filter on the Issue Search navigator but no issues will be displayed. When trying to search issues from restricted projects it will show No issues were found to match your search.