GtkDragSource

static void
my_widget_init (MyWidget *self)
{
  GtkDragSource *drag_source = gtk_drag_source_new ();

  g_signal_connect (drag_source, "prepare", G_CALLBACK (on_drag_prepare), self);
  g_signal_connect (drag_source, "drag-begin", G_CALLBACK (on_drag_begin), self);

  gtk_widget_add_controller (GTK_WIDGET (self), GTK_EVENT_CONTROLLER (drag_source));
}

static GdkContentProvider *
on_drag_prepare (GtkDragSource *source,
                 double         x,
                 double         y,
                 MyWidget      *self)
{
  // This widget supports two types of content: GFile objects
  // and GdkPixbuf objects; GTK will handle the serialization
  // of these types automatically
  GFile *file = my_widget_get_file (self);
  GdkPixbuf *pixbuf = my_widget_get_pixbuf (self);

  return gdk_content_provider_new_union ((GdkContentProvider *[2]) {
      gdk_content_provider_new_typed (G_TYPE_FILE, file),
      gdk_content_provider_new_typed (GDK_TYPE_PIXBUF, pixbuf),
    }, 2);
}

static void
on_drag_begin (GtkDragSource *source,
               GdkDrag       *drag,
               MyWidget      *self)
{
  // Set the widget as the drag icon
  GdkPaintable *paintable = gtk_widget_paintable_new (GTK_WIDGET (self));
  gtk_drag_source_set_icon (source, paintable, 0, 0);
  g_object_unref (paintable);
}