Instead of:
$select = wp_dropdown_categories('show_option_none=Select category&show_count=1&orderby=name&echo=0');
put this:
$select = wp_dropdown_categories('show_option_none=Select category&show_count=1&orderby=name&echo=0&child_of=" . $ID_OF_PARENT_CATEGORY);
where $ID_OF_PARENT_CATEGORY is a variable holding the ID of parent category, from which you want to show the children.
Showing parent
That category WON”T show. To show it, you must do some greater hack (here I’ll show you only thing that I can think right now), since there are no argument like include, so that you can just include it.
You can show categories that are PARENT and it’s siblings, so, you will show children of PARENT’s parent. That means that you will put in args ‘show_option_none=Select category&show_count=1&orderby=name&echo=0&child_of=”.$ID_OF_GRANDPARENT.”&exclude=”.implode(“,’, ARRAY_OF_PARENTS_SIBLINGS)