Mail app will not let me sign in

If the Mail app on your iPhone is not letting you sign in and the "next" button keeps reappearing, there may be an issue with your Apple ID or with the Mail app itself. Here are some things you can try to troubleshoot the issue:

1. Make sure that you are entering the correct Apple ID and password. The Apple ID and password are case-sensitive, so make sure that you are using the correct upper- and lower-case letters.
2. Check your internet connection. The Mail app requires an internet connection to sign in, so a weak or unstable connection could cause issues.
3. Restart your iPhone. This can sometimes resolve issues with the Mail app. To restart your iPhone, press and hold the power button until the "slide to power off" slider appears, then drag the slider to turn off your device. After your device turns off, press and hold the power button again until you see the Apple logo.
4. If you are still unable to sign in to the Mail app, you may want to try deleting and reinstalling the app. To delete the Mail app, press and hold the app icon until the icon starts wiggling
5. If none of the above steps help, you may want to try contacting Apple Support for further assistance. You can do this by visiting Apple's Support website at Official Apple Support,

I hope this information helps. If you have any other questions, please don't hesitate to ask.