How get posts from a subcategory of a category by name?

// Getting Parent ID
$parent = get_term_by( 'name', 'Session 2015', 'category');

// Checking if SubCategory Exist. 
$term = term_exists('Photos', 'category', $parent->term_id);

//if Exist Do the query
if ($term !== 0 && $term !== null) {
  $query = new WP_Query( 'cat=".$term["term_id'] );
}

References:

• term_exists

• get_term_by