I've got a document library and in this library, each document has different permission and some users are limited. So, when a document updates, I want to alert only the users that have permission. In other words I want to use alert item-level permission.
Normally the alert works only in items of which you have visibility, so you could set alerts on the whole list and the permission models will sort out if to send out emails to who. I have tried in the past to set alerts on people who were NOT in the permissions of the site and they never received any alert.
I suggest you use a workflow which is triggered by an item being modified.
You can target the email to be sent to specific Sharepoint User Groups.
Alerts are pretty basic and you can not do much with them, whereas a workflow is more flexible.
It might be worthwhile to think about changing the way the document library or perhaps Sharepoint Site works. Can the individual permissions on each item be removed? Perhaps defining Sharepoint Groups would allow you to achieve the same outcome without needed to make unique permissions on each item?
Perhaps you could consider classifying the documents by creating a choice column - then tag each item according to a property. For instance if the documents are used by different departments, tag each document with the department name. Then customise a workflow to reference the choice (e.g. if Department field = Accounts, email the Accounts Group).
You can set alert on a document or an item. Please ensure that particular item is select before setting alert. A very good tutorial is available here
Select the item you would like to set an alert:
Note the title of the document
I have tested setting an alert to a user with only 'Read' permission and this user did receive an email confirming the item has changed. I tested this on the SharePoint Online.