Is it permissible to take money from the company's custody to cover the maintenance costs of the car used for work without the employer's knowledge, especially since its use saves the company large sums of money?

It is not permissible to take an amount from company funds for the maintenance or fuel of a private car without the company's approval. This is considered a betrayal and an unlawful appropriation of money, based on the words of Allah the Almighty: "O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know [the consequence]." One can refrain from using their private car and request a company car, or agree upon compensation for its use.