Showing 'CTnotifyUIservice' when reviewing screen time in iPhone

If you feel an unauthorized person/app is remotely using, controlling or monitoring your device, then that is possible only if you have done one or more of the following Don'ts...

1. Don't hand over an iPhone to kids or to a stranger without Enabling Guided Access
2. Don't share Apple IDs
3. Don't Jailbreak
4. Don't share sensitive information pertaining to your device
5. Don't give in to Phishing
6. Don't plug in your device in Airports and Public places through third-party cables and trust the device. Beware of Juice Jacking. (Especially in India)
7. Don't leave your iPhone unlocked and unattended in public places like offices, schools, malls, etc.

If one of the above is true then quickly change the Apple ID Password and Return iPhone settings to their defaults.

Keep the iPhone updated to the latest iOS always and never Jailbreak. That's it.

iOS / iPadOS devices cannot be hacked or infected with Virus / Malware / Spyware *** unless you have intentionally downloaded spurious software or unauthorized apps directly from the internet and installed them on your device or/and have Jailbroken. 

It (Hacking) also depends on how careful you are in sharing sensitive and valuable information pertaining to your iPhone such as Passcode, Password, etc with your friends and family members.

Be judicious when sharing the device's sensitive and valuable information with friends and family members.

**The primary reason for this is Sandboxing. All third-party apps are “sandboxed”, so they are restricted from accessing files stored by other apps or from making changes to the device. Sandboxing is designed to prevent apps from gathering or modifying information stored by other apps.

Security of runtime process in iOS and iPadOS - Apple Support

The sandbox on an iPhone is a security feature that creates a restricted environment for each app to run in isolation from other apps and the operating system. It is a core component of iOS's security architecture and plays a crucial role in making iPhones more secure.

If you doubt the authenticity of the information provided earlier, you have two alternatives:

1. Report the hacking incident to local law enforcement authorities and actively pursue the case.
2. Accept the credibility of the information; it is impervious to hacking. Just as some individuals hold unconventional beliefs, such as a flat Earth or moon landing denial, one has the freedom to believe in anything. The choice ultimately rests with you in this open and free world.

To improve my understanding of the phenomenon, it would be highly beneficial if you could share a full screenshot (Do not crop it). Visual representations carry a greater impact than written descriptions.

Please remember that this is a public forum, so when attaching a screenshot, please avoid including any personal credentials such as IP addresses, card details, email IDs, Apple IDs, IMEI numbers, serial numbers, phone numbers, order IDs, or any identifiable location information if you are sharing a map.

With the limited information that you have provided, It is hard to even guess the problems faced by you. 

You may get faster and better responses to your query by --> Writing an effective Apple Support Commun… - Apple ...

Please re-post with detail so that someone else can help.