You should not be prompted to sign in to the store unless you are trying to make a purchase. You can go into Settings>General>Restrictions and set up restriction for the iTunes Store. That very well could stop the prompt.
It is for sure that you can't sign into iTunes Store without an Internet connection. To check if your device is connected to the Internet, please try to open a website with a browser and see if it can connect to any website. If no, go to Settings > Cellular, make sure cellular is enabled for iTunes Store.
Here's how to sign in to an account: Tap Settings on your iPhone. Scroll down and tap iTunes & App Stores; the screen shown appears. Tap Sign In, and enter your Apple ID and password, then tap the Sign In button.
Sign in to the iTunes Store
Apple's online store for purchasing music, movies, TV shows, e-books, podcasts and audiobooks for the iPhone, iPod touch and iPad. Apple's App Store is also available from the iTunes store.
Solution 1: Arrange the Settings of iTunes & App Store And for free downloads, the App Store keeps asking for passwords probably because you turned on the Require Password. If you don't want to enter passwords when you download free items, you can turn it off.
So is iTunes and App Store the same? From a platform-specific perspective, no. From a functional perspective, yes. iTunes sells apps optimized for iOS based devices such as iPads, iPhones, and the iPod touch.
Restore iPhone in Mojave or older (or on a PC)
Answer: A: Answer: A: Go to Settings > iTunes & App Stores > Tap your Old Apple ID > Tap Sign out.
Here's how to sign in to an account:
If you need to sign in or out of the App Store® on your Apple® iPhone®, follow these step-by-step instructions.
At the General screen in the Watch app, turn on the switch for Automatic App Install. Next, go to the My Watch section in the Watch app on your phone. Swipe down the screen and tap the entry for App Store.
Buy music from the iTunes Store