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 this, please proceed with adding fee options (at the Options tab) and supplementary conditions like scope or calculations, then the fee can be saved.
Now the fee can be tested on the storefront. If you go to the store and proceed to checkout, you'll see your fee like so:
If you try to proceed without selecting a fee option, you'll get a message asking to select it first: