The simplest solution that often fixes this is to remove and re-add the email account on your Apple devices, but you should try just updating the password first.
If Just Changing the Password Doesn't Work
If you still can't send or receive emails, you may need to check the server settings or remove and re-add the account.
1. Verify/Update Server Settings
Your Road Runner email address is now managed by Spectrum. The correct IMAP/SMTP settings (which are generally recommended for multiple devices) are:

You may also see server addresses like mobile.charter.net or mail.spectrum.net depending on your exact domain (the part after the @), but mail.twc.com and smtp.twc.com are very common for Road Runner accounts.
Remove and Re-add the Account
If the simple password change or settings check fails, deleting the account and adding it back usually resolves any lingering configuration issues.
- Go back to Settings > Mail > Accounts.
- Tap on your Road Runner/Spectrum account.
- Tap Delete Account (this only removes the account from the device, not the emails on the server).
- Go back to Settings > Mail > Accounts > Add Account.
- Choose Other.
- Select Add Mail Account and enter your Name, Full Road Runner Email Address, and your New Spectrum Password.
- The device should automatically try to find the settings. If it fails, you'll be prompted to enter the IMAP/SMTP settings from the table above.
Note: Always use your full Road Runner email address (e.g., user@nycap.rr.com) as the Username for both the Incoming and Outgoing Mail Servers.