How to stop the App Store from asking for a billing information when I don’t have one and won’t be adding one

1.

You may need to have a valid payment method on file, even if the app you want to download is free.

Free apps has also In-app pruchase.

2.

If you don't have a credit card or don't want to use a credit card, you can also use your Apple Account balance as payment method.

See -> What you can buy with your Apple Gift Card or Apple Account balance

What you can buy with your Apple Gift Card or Apple Account balance – Apple Support (UK)

and ⤵️

• You can't use your Apple Account balance to send gifts or gift cards.
• If you use Family Sharing, your family members can't spend your Apple Account balance. Funds that you add to your Apple Account balance are only available to you. Find out more about how purchases are billed to your Apple Account balance.
• Some purchases might require you to have a credit card on file, even if you use your Apple Account balance to make the purchase.

See also -> How to redeem your Apple Gift Card or App Store & iTunes gift card

How to redeem your Apple Gift Card or App Store & iTunes gift card – Apple Support (UK)

When redeeming a gift card, the amount will be credited to your (1) Apple Account balance and (2) you need to set your Apple Account balance as your default payment.

(1)

See -> Check your Apple Account balance

Check your Apple Account balance – Apple Support (UK)

(2)

See -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

If you already use your Apple Account balance, the Apple Gift Card or App Store & iTunes gift card is automatically added to your Apple Account balance.

If you're still unable to update your payment method, Contact Apple Support.

See also -> Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)

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If you have a valid payment method on file, instead of buying or order an App Store & iTunes gift card, you can Add money to your Apple Account balance anytime, no gift card needed, see -> Apple Gift Card - Apple (UK)

Where to buy a physical Apple Gift Card or App Store & iTunes gift card: actually, you can buy an Apple gift card at many places, at an Apple Store or an Apple Authorized Reseller in your region.

See also this Apple article:  If you can't redeem your Apple Gift Card or App Store & iTunes Gift Card

If you can't redeem your Apple Gift Card or App Store & iTunes Gift Card - Apple Support

Beware of -> About Gift Card Scams -> About Gift Card Scams - Official Apple Support 

If you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.