What is the ruling of Islamic law and what must I do regarding documenting my third divorce, knowing that this is the first time I have divorced her, and can I reverse this mistake?

If you divorce your wife with a single pronouncement, such as "You are divorced," it is considered a revocable divorce, and you may take her back as long as she is within her waiting period (iddah). However, if the registrar wrote down three divorces, then you must consult the registrar and the court to correct the error due to the widespread corruption this would cause in lineage and inheritance. If the divorce was in exchange for financial compensation, then it is a khulʿ (divorce at the wife's instance), which is irrevocable, but you may remarry her with a new contract.