Try this
$args = array(
'child_of' => 11,
'hide_empty' => 1
);
$categories = get_categories($args);
foreach ($categories as $category) {
echo "<li ><a href='#' data-filter='.".strtolower($category->name)."'>".$category->name."</a></li>";
}
You may use $category->slug
for that data-filter
purpose