Hi JKRMaya,
Thanks for posting your question. I see you're being prompted to sign in to complete a purchase from your Apple Watch, and I'm happy to see if I can assist.
Typically, this type of alert would come up if an app was downloaded using a different Apple ID. It may help to try the steps below in order to determine which app is causing the prompt. I recommend updating your apps one at a time to see which one brings up the prompt: Install apps on your Apple Watch
"How to check for updates on your Apple Watch manually
- Open the App Store on your watch and scroll down to the bottom.
- Tap Account.
- Tap Updates.
- Tap Update next to an app to update only that app, or tap Update All."
I hope this helps get you started. Take care.