purchased app by mistake
my child purchased the app by mistake
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Apple's terms of purchase in the USA are, "All Transactions are final" (https://www.apple.com/legal/internet-services/itunes/us/terms.html), but some countries have different laws so check terms for your country at: http://www.apple.com/legal/internet-services/itunes/. If sales are final then it is Apple's decision if they want to grant a refund. You can always ask, and people do get refunds on a case by case basis, but Apple can also say no.
Get help with an item purchased from the App Store, iTunes Store, or iBooks Store - https://support.apple.com/HT204084
Report a Problem - http://reportaproblem.apple.com - "Sign In for help with iTunes purchases made in the last 90 days"
If a reporting a problem request is unsuccessful you can also try:
Other ways to contact iTunes Support:
https://www.apple.com/emea/support/itunes/contact.html
https://support.apple.com/country-selector/itunes
How to use parental controls on your child‘s iPhone, iPad, and iPod touch - https://support.apple.com/HT201304 - including what to do if you forgot the passcode (see also: https://discussions.apple.com/thread/7846481?answerId=31330560022#31330560022)