still requesting my “new” password,
When?
After you change your password?
If yes, see this Apple article: What to do after you change your Apple ID or password
What to do after you change your Apple ID or password - Apple Support
When you want to download an app?
If yes, see this Apple article: Require a password for App Store and iTunes purchases
Require a password for App Store and iTunes purchases - Apple Support
Or may be you need to check your payment method, see the following Apple articles:
If you can’t download or update apps on your iPhone or iPad
If you can’t download or update apps on your iPhone or iPad – Apple Support (UK)
-> You may need to have a payment method on file, even if the app you want to download is free.
Check which payment method you have on file and make sure it hasn't expired, been declined or failed.