Na sua cláusula where, altere new.id para old.id
-- Trigger DDL Statements
DELIMITER $$
USE `db_dhruniversity`$$
CREATE
TRIGGER `db_dhruniversity`.`ai_delete_course`
AFTER DELETE ON `jos_jquarks_quizzes`
FOR EACH ROW
BEGIN
DELETE FROM jos_jquarks_courses
WHERE (quiz_id = old.id);
END$$
