Deleting an app does not cancel a subscription if there is one. You must cancel the subscription:
View, change, or cancel your subscriptions - https://support.apple.com/HT202039 - "Your membership or subscription might renew if you don't cancel your membership or subscription more than 24 hours before your renewal date." At this stage the renewal is considered a purchase. For a new subscription the sale is probably effective from when you first agree to subscribe.
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. To request a refund:
Get help with an item purchased from the iTunes Store, App Store, Mac App 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"
Other ways to contact iTunes Store Support:
https://support.apple.com/contact
https://www.apple.com/emea/support/itunes/contact.html
If by third party subscription you have subscribed with Norton directly, not through Apple, then you will have to deal with them. Go to their web site and see how to do this.