Hey there, Trammer!
Thanks so much for using Apple Support Communities.
We want to make sure your devices are all working as expected, including those Apple Watch prompts. To clarify, do you currently use an Apple Watch at all? Or is the iPhone prompting you to connect a device that you do not own? If you do have an Apple Watch, we would recommend that you try to erase and pair that watch again to see if this helps resolve those unexpected prompts. Here's where to start: Unpair and erase your Apple Watch
If you don't have an Apple Watch at all, we'd recommend that you update your iPhone to the latest version of iOS and see if that helps: Update your iPhone, iPad, or iPod touch
We hope that this information is helpful.
Have a great day!