AT Internet doesn't have a default "Push" source.
It is however possible to classify traffic from push campaigns in its own separate source.
Thanks to the self-declaration of sources and campaigns since smarttag 5.29.2 and the new Piano analytics SDK, you can use a custom source without declaring it before.
You can use it in a tagged link with the following parameters, for example:
The "Push" source will be available as a marketing source in Piano Analytics.
As with any traffic source, it will only be taken into account if the visitor isn't already on your site (if a visit is ongoing, clicking on a push notification will not change the visit's source).
Additional information for Android and iOS:
SDK Piano Analytics