Provided you did not do an instant payment / the payment has not cleared yet, then you can still cancel the transaction and in effect, cancel the order with the company as well.
I don't think there's any way to cancel a transaction paid for by debit card.
Unless the deadline was soon, it is disturbing that the order (a dissertation) could not be cancelled less than 24 hours after being placed.
Correct. However, the OP never indicated the due date requested. It's not unheard of for customers to order a 100-pg dissertation with a 1-week deadline. That kind of thing does require the writer to start immediately, in which case, the company (or writer) has the right to retain
pro-rata payment for whatever work has already been done before the cancellation request. Otherwise, in normal situations with a long-term dissertation-appropriate deadline, there's no excuse for not allowing the refund. When I was writing for essay companies, I'd occasionally get system notices from the company that a project on my calendar had been cancelled; but if it was a long project and/or a short deadline, I'd get an email from admin first, asking me whether I'd started the project.