How to display child term of current term’s parent taxonomy?

I think you can just use get_terms() for this. This is just some bare minimum code, I guess you also want to add permalinks, term description or other things.

However, I just tested this code (now tested with taxonomy “course”) and it works.

I try my best to comment the code as we go along:

// our current taxonomy slug
// If you want to get the current taxonomy automatically try using $wp_query->get_queried_object();
    $taxonomy = 'course';

// we get the terms of the taxonomy 'course', but only top-level-terms with (parent => 0)
$top_level_terms = get_terms( array(
    'taxonomy'      => $taxonomy,
    'parent'        => '0',
    'hide_empty'    => false,
) );

// only if some terms actually exists, we move on
if ($top_level_terms) {

    echo '<ul class="top-level-terms">';

    foreach ($top_level_terms as $top_level_term) {

        // the id of the top-level-term, we need this further down
        $top_term_id = $top_level_term->term_id;
        // the name of the top-level-term
        $top_term_name = $top_level_term->name;
        // the current used taxonomy
        $top_term_tax = $top_level_term->taxonomy;

        // note that the closing </li> is set further down, so that we can add a sub list item correctly
        echo '<li class="top-level-term"><strong>'.$top_term_name.'</strong>';

        // here we get the child-child terms
        // for this we are using 'child_of' => $top_term_id
        // I also set 'parent' => $top_term_id here, with this line you will only see this level and no further childs
        $second_level_terms = get_terms( array(
            'taxonomy' => $top_term_tax, // you could also use $taxonomy as defined in the first lines
            'child_of' => $top_term_id,
            'parent' => $top_term_id, // disable this line to see more child elements (child-child-child-terms)
            'hide_empty' => false,
        ) );

        // start a second list element if we have second level terms
        if ($second_level_terms) {

            echo '<ul class="second-level-terms">';

            foreach ($second_level_terms as $second_level_term) {

                $second_term_name = $second_level_term->name;

                echo '<li class="second-level-term">'.$second_term_name.'</li>';

            }// END foreach

            echo '</ul><!-- END .second-level-terms -->';

        }// END if

        echo '</li><!-- END .top-level-term -->';

    }// END foreach

    echo '</ul><!-- END .top-level-terms -->';

}// END if

Also try using print_r($top_level_term); for example in the first foreach loop. With that, you can see all the info that comes with one single term.

I would say you should use this code in the normal taxonomy archive template and don’t use the file taxonomy-course-photoshop.php. Because then you would need a separate template file for every single term, and that’s not practicable.

Edit:
Also, make sure you have some posts assigned to the single terms and sub-terms. Otherwise, the terms will not display at all!

Update:
Yes, you can get the current taxonomy and term data automatically.

If you are working inside taxonomy-course.php than you can try this:

        //get the current object
        $current = $wp_query->get_queried_object();

        // try  var_dump($current);  to see all available data!

        // return the ID of the current term
        // i.e. ID of term "Photoshop" is "26", so we get "26" if we are viewing "Photoshop"
        $current_term_id = $current->term_id;

        // return the nicename of the current term
        // i.e. returns "Photoshop"
        // or "ps-thematic#1" if we are on a child term of "Photoshop"
        $current_name = $current->name;

        // returns the current taxonomy slug we are in
        // i.e. it will return "course"
        $current_taxonomy = $current->taxonomy;

        // returns the ID of the parent, if we have a parent
        // i.e. if we are viewing "ps-thematic#1" it will return the ID of "Photoshop", 26
        // if we are viewing "Photoshop", it will return 0, because "Photoshop" is a top level term
        $current_parent = $current->parent;

        // display name of current term, i.e. "Photoshop"
        echo '<strong>'.$current_name.'</strong>';

        $sub_terms = get_terms( array(
            'taxonomy'      => $current_taxonomy,
            'child_of'      => $current_term_id,
            'hide_empty'    => false,
        ) );

        // only start if some sub terms exist
        if ($sub_terms) {

            // try  var_dump($sub_terms);  to see all available data!

            echo '<ul class="sub-terms">';

            foreach ($sub_terms as $sub_term) {

                // try  var_dump($sub_term);  to see all available data!

                // only show the name for the example, "ps-thematic#1"
                echo '<li>'.$sub_term->name.'</li>';

            }// END foreach

            echo '</ul><!-- END .sub-terms -->';

        }// END if

So if we are viewing “Photoshop”, the above function shows ONLY:
Photoshop
– ps-thematic#1
– ps-thematic#2

It does NOT show “After Effects” or the children, ae-thematic#1 or ae-thematic#2.

Also take a look using var_dump($current);.
You will see all available information. As you will see above, for example, I left some code in the function $current_parent = $current->parent;.
For example you could check:

            // check if current parent is not = 0
            if ($current_parent != '0') {
                // code if parent is NOT 0
                // that always means that we are viewing a child
            } else {
                // code if parent is 0
                // if parent is 0 we are sure we are on a top level
            }

But there are some more infos/data in $current that you can maybe use.
I Hope this helps.