If you need your customers to select an obligatory fee during checkout, you can create a mandatory fee that won't allow customers to place an order unless at least one fee option is selected. To do that, please go to Magento Admin Panel → Stores → Configuration → Amasty Extensions → Extra Fee → Fees, click Add New Fee button, and switch the Mandatory to select the option to Yes.
After that, proceed with adding fee options (at the Options tab) and other settings like scope or calculations, then the fee can be saved.
When the fee is configured and saved, you can go to the store and proceed to checkout to see how the fee works.
If you try to proceed without selecting a fee option, you'll get a message asking to select it first: