How can you tell if someone is spying on you through your phone?

If you haven't jailbroken your iPhone, it's not possible.

See ->  Share your screen in FaceTime on your iPhone or iPad

Share your screen in FaceTime on your iPhone or iPad - Apple Support

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Everyone can see what's on your screen until you stop sharing, but they can't control anything on your device. If you get any notifications while sharing your screen, others won't be able to see them.

When you're sharing your screen, others won't be able to see content that requires a subscription, a free trial, or a purchase or rental to view. 

To keep your Apple ID account secure, see the following Apple articles:

Manage and use your Apple ID

Manage and use your Apple ID – Apple Support (UK)

See who has access to your device or accounts

See who has access to your device or accounts – Apple Support (UK)

Recognize and avoid phishing messages, phony support calls, and other scams

Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

Phony "tech support" / "ransomware" popups and web pages

Phony "tech support" / "ransomware" popup… - Apple Community

Identify and filter junk mail in iCloud

Report and block spam in iCloud mail - Apple Support

If you think your Apple ID has been compromised

If you think your Apple ID has been compromised - Apple Support

Identify legitimate emails from the App Store or iTunes Store 

Identify legitimate emails from the App Store or iTunes Store – Apple Support (UK)

Set up iCloud Keychain

Set up iCloud Keychain - Apple Support

Create a strong password for your Apple ID, It is best if your password consists of eight or more characters and include upper and lowercase letters, and at least one number. You can also add extra characters and punctuation marks to make your password even stronger. 

Never provide your password, passcode, security questions, verification codes, recovery key or any other account security details to anyone else. Apple will never ask you for this information.

See also the following Apple articles:

About the 'Trust This Computer' alert on your iPhone, iPad, or iPod touch

About the 'Trust This Computer' alert on your iPhone, iPad, or iPod touch - Apple Support

Authorize or deauthorize your computer for iTunes Store purchases

Authorize or deauthorize your computer for iTunes Store purchases - Apple Support 

Get a verification code and sign in with two-factor authentication

Get a verification code and sign in with two-factor authentication - Apple Support

Check your Apple ID device list to see where you're signed in

Check your Apple ID device list to see where you're signed in - Apple Support

• if you see devices that don't belong to you, delete from your account.