Syncing of notes

See this article Upgrade your Notes app - Apple Support

To use the latest Notes features, all you have to do is upgrade.

When you update your device to iOS 9 and later or OS X El Capitan and later, and open Notes for the first time, you see the option to upgrade. Choose Upgrade Now, then both your notes on your device and your notes on iCloud.comupgrade. And if you sign in to iCloud with the same Apple ID on your other devices with the latest version of iOS and macOS, any changes you make to a note on one device instantly appear on all your other devices.

Make sure that your notes finish upgrading before you leave the Notes app.

Make sure you must have an Apple ID see this article Sign in with your Apple ID - Apple Support

And also have to set up iCloud account Set up iCloud on your Mac - Apple Support

Read these articles iCloud: Set up iCloud on your iOS devices or your Mac or Windows computer

Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB - Apple Support

What you can sync with iTunes

Contacts and calendars.

And if you still can't sync see this article Update your iPhone, iPad, or iPod touch - Apple Support