Create an Apple ID for your child - https://support.apple.com/HT201084
It is free. However, if you need to create an account for a minor child you do have to set up Family Sharing and part of that is entering a credit card or other valid payment method. Again there is no charge but some people misperceive this as having to pay. Also a amall amount of ~$1 may be a temporary authorization hold that will be refunded (pending charge ➞ https://support.apple.com/HT201292 ).
The next document may also interest you.
Approve what kids buy with Ask to Buy - https://support.apple.com/HT201089