Recipients Settings
Switch to the Recipients tab. Here you can add a list of recipients who will receive this alert.
By default the alert is sent to the Alert author. To send alerts to other users you need extended permissions. In To, CC and BCC you can add users and groups, list fields that contain users (Assigned to, Created by…) and external e-mail addresses; with Contact List you can add the contacts of a SharePoint contact list. Enter From and Reply To addresses if needed.
Without extended permissions the To field contains only Alert author, and Contact List, CC, BCC, From and Reply To are hidden. Extended permissions have site collection administrators, users with Full Control on the site and members of the groups selected in Site groups of the General Settings.

You can also send alerts to users from a SharePoint Contact list.
Click + next to Contact List and choose the Location (the site), the Name (the list) and the List View. Only the contacts shown in the selected view and with a filled E-mail column receive the alert; use the view to filter the recipients.
Next, you can add optionally field values for carbon copy and blind carbon copy. These fields have the same rules to add addresses as the field “To”.

Note: Please ensure the smtp server is properly adjusted and doesn’t have security restrictions, which are interrupting alert email delivery.