Hi salimah80,
Thanks for coming to Apple Support Communities for help today.
From what we can see the Badges switch should be available in Settings > Notifications > Mail.
We'd suggest restarting the iPhone. This can often resolve minor issues.
We also notified you posted in the business and education forum. Do you have a profile installed from a company or institution? If you do, this can prevent some features from being available. You can check in Settings > General > VPN & Device Management.
Let us know more details if that doesn't explain the issue. We also aren't quite clear about the part regarding Apple Watch and iPhone if you could expand on that further and why you think it could be related.
Have a fantastic day!