There is no OOB feature to set a Notification / Message on Portal Pages.

We can create a custom Notification entity to create your notifications

in the Portal Header Web Template (after the profile navigation menu), can add a FetchXML to retrieve this records and show a bell icon (or any custom icon)

{% assign countNotification = query.results.entities.size %}

   <li>

    <a class="navbar-icon" href="{{notificationUrl}}" role="button" aria-haspopup="true" aria-expanded="false" aria-label="{{ snippets["Header/Notification/ToolTip"] }}" >

   <span class="glyphicon glyphicon-bell"></span><span id="notificationcount" class="badge badge-pill badge-danger">{{ countNotification }} </span> 

   </a>

</li>

4064.notification.PNG