Why is my iPhone vibrating randomly every few minutes

Check Settings > Sounds

If your settings are as they should be, try the troubleshooting help here > iPhone Won’t Stop Vibrating? Here’s How to Resolve the Endless Buzzing

A quick detail to add to Carolyn's answer:

As she says, check Settings > Sounds, but in particular, check Settings > Sounds > New Mail > Vibration.

From what you've said, that sounds like the likely culprit to me.

What’s interesting is that my email is set to fetch manually. So if my phone is vibrating because I have new mail, then is checking for email when I’ve specfically set it not to. Plus when it vibrates, the email icon doesn’t indicate I have new mail. I also believe this is a recent behavior. I have changed this setting, so we’ll see if this works. But whether it vidrates or not it would seem it’s not honoring the fetch manually setting which impacts battery and cell usage.

Thank you, this was really helpful and in my case corrected the issue.

J