Conference Joy only serves as a conference management tool for the conference admin. It is not responsible for hosting the conference. Your conference admin is the one who receives the payment of your registration fee and they are responsible for refunding the fee, if that is a part of their conference's policy. Please contact your conference admin to resolve any fee-based issues.
Note that the processing fee is NOT refundable as Conference Joy is charged by Stripe for every transaction. So you will receive whatever fee your conference admin agrees to refund you, minus the processing fee.