How can one atone for swearing a false oath on the Qur’an and repeating the sin, despite sincere repentance?

You must perform sincere repentance by abandoning the sin, regretting it, and resolving never to return to it. You must also conceal your sin and not disclose it, as the Messenger of Allah, peace and blessings be upon him, said: "Whoever commits any of these abominations, let him conceal himself with Allah's concealment; for whoever exposes his deed to us, we shall apply Allah's punishment to him." It is permissible for you to lie to conceal yourself, but it is better to use equivocation (Tawriya) in an oath, because necessities permit the forbidden.