Is there anyway how to create a project which will be accessible for one user only? I mean there won't be the way for administrators seeing the tickets at all.
You would have to assign that user a unique rol and make that project accessible only for people in that role (so, your one user).
So... technically it can be made but it seems you might be the user you want to have "exclusive" access to that project and you are not an admin so this isn't likely to be the answer you were hoping to get. And regardles of the configuration "now" a sysadmin could allow him/herself to see that project at any time. That's why he/she is there, to configure this kind of stuff.
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