How do I delete a child Apple Account from my iPhone?

For a complete answer we would need more context under which the child signed in. Did the child just borrow your device(a very bad idea) or was a child using this device long-term and is now returning it to you?

Get the child to sign out. The process is similar to signing in as described at this link --> https://support.apple.com/HT204053

If the child has been using this device for a long time and you now want to make it your own device, read this article --> What to do before you sell, give away, or trade in your iPhone or iPad = https://support.apple.com/109511