Hi I'm trying to find a way to make an specific item visible for only one specified user of the site.
Has anybody any idea?
You can assigne the unique permissions for an user, but
When there are many unique permissions in a list then it can reduce the overall performance of the query so that isn’t recommended. The number of unique permission in a list gets bigger over time and that reduces the performance. While the limit is by default 50,000 it is ideal if you make your customized limit 5,000.
see this post.
Set the permissions of the item to only allow that one specific user access.
This will not prevent Site admins from seeing the item, but that's the best you can do.
In the browser on a view where you have the item select Manage Permissions in the dropdown next to the name. In the permissions page click Stop Inheriting Permissions in the ribbon. Add the user giving her/him the right rights. Remove all other users/groups.