Is there any way to call custom API while saving the page type

You should be looking into the Global event handlers (https://docs.kentico.com/k10/custom-development/handling-global-events)

In there you can check for you specific page type and do custom actions.

In your DocumentEvents.Update.After += Document_Update_After; event:

You can check the type like:

private void Document_Update_After(object sender, DocumentEventArgs e)
    {
        if(e.Node.NodeClassName == "abc.YourPageType")
        {
             // Add custom actions here
        }
    }