Is it permissible to deduct the amount of zakat that was mistakenly paid via a check that has not been cashed for four years, from this year's zakat?

If a person demands a financial right from you that is due to them, and they had not borrowed from you, then the zakat on the demanded money is due on them, not on you. If you paid zakat on this money, assuming it was yours, and then it became clear that they had not withdrawn the amount, it is not permissible to deduct that zakat from this year's zakat, and what you paid will be considered an act of charity for you.