AppStore login issue

If you can't connect or sign in to iCloud or your account, Apple has a list of things you can try in the document If you can't connect or sign in to iCloud - Apple Support

If you are using a VPN, try turning it off and see if you can then log in. E.g., AppStore - Apple Community

For more assistance try the iCloud Support web site --> iCloud - Official Apple Support

If you still have problems try official Apple Support. Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> Contact Apple for support and service - Apple Support

Including basic information in your post will assist us in quickly finding a specific answer to your question. Provide a clear description of what you are trying, where it fails to perform as expected, and the exact wording of error messages. Include your hardware year and model information if you have not already done so in the posting information.

You are sign in here .  .  .  with your Apple ID & Password.

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.

What happens when you use the same Apple ID & Password that you use to sign in here?

See the following Apple articles

Sign in with your Apple ID -> Sign in with your Apple ID - Apple Support

Manage and use your Apple ID -> Manage and use your Apple ID – Apple Support (UK)