Hi @pagol
I’m not sure if I understand your explanation, so please forgive me if I’m wrong.
To show the image for the child category, I believe you can do it like this:
$current_term = get_queried_object();
$image = get_field('cat_thumbnail_image', $current_term );
echo '<div class="test">'.$image.'</div>';
If that is not what you want, could you please share some screenshots of the issue with notes on how you want it to be?
Thanks 🙂