Create an account for children under 13

As you have probably discovered, to set up an ID for a minor requires this be done with Family Sharing active which requires the organizer have a payment method present. If you wish to limit your child's used of your card, set up Ask To Buy:

Approve what kids buy with Ask to Buy - Apple Support

Create an Apple ID for your child - Apple Support

I see the recommended solution has been deemed to be the referring article that you had already read before coming here, and apparently didn't answer your question. Note that my post tells you one way how to have "parental control over the account" which is not something mentioned in the Apple ID for your child document, and maybe assuages your concerns about using a credit card by using Ask To Buy. If your concern is unfettered use of your card then set up Ask To Buy as I indicated but only if you dare read beyond what has been recommended for you to read and just tells you to read what you have read already anyway.

To set up an Apple ID for a child under 13 you have to do so by setting up Family Sharing which requires a payment method such as credit card. No options. That's the article that you read before posting here, then was recommended twice*. Now of course you don't say how old your son is and maybe you don't need to do this under Family Sharing but as for an adult How to create a new Apple ID - Apple Support. You can set up Ask To Buy for children up to 17 years of age.

Not sure how you attempted to create the account, but assuming you want to have the maximum parental control over the account...

https://support.apple.com/en-us/HT201084

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