Will a person be held accountable for not reprimanding underage children who utter something forbidden or mock a word from the Qur’an or the religion, and is not reprimanding considered disbelief?

The child is not held accountable, so he cannot be judged as an infidel, because the Prophet, peace and blessings be upon him, said: "The pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty, and from the insane until he regains his sanity." No one has ever said that failing to rebuke a child is an act of disbelief. Therefore, stop your obsessive thoughts of excommunication, and be eager to teach and advise these young boys.