Hi there arrie224,
Thank you for posting to Apple Support Communities.
We understand that you're being asked to sign into your Apple ID repeatedly on your new iPhone. We'd like to help.
Check if you can log in successfully to your Apple ID at the Apple ID webpage: Apple ID
If you're able to log in successfully, we recommend restarting your iPhone to then see if the issue continues. If it does, we recommend ensuring that your iPhone is up-to-date with the latest iOS software. Before updating, we recommend backing up your iPhone first. These articles can be of help. When you back up, you can back up using a Mac or PC rather than iCloud if you choose.
How to back up your iPhone, iPad, and iPod touch
Update iOS on iPhone
If your iPhone is updated and you're still having an issue, we recommend contacting Apple Support
Have a good day.