Family sharing
How can I add a child on family sharing without paying?
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It doesn't cost anything to add the child to Family Sharing.
If you are asking how to add child, but not be responsible for paying for their purchases, you can't do that. The Family organizer is responsible for paying for all purchases. What you can do is have them buy/redeem iTunes Gift cards to the account. Charges will be deducted from the account balance before the organizer's credit card is charged. See the Apple Support article(s) below.
App Store & iTunes Gift Cards by Email