How do I request a new apple ID

You can create one. See How to create a new Apple ID https://support.apple.com/en-us/HT204316

Did you try a password reset?

Where are you trying to sign in? What is the exact error message you are seeing?

You have an Apple ID but want to start another one?

See Change your Apple ID (Be very aware of the restrictions here.)

https://support.apple.com/en-us/HT202667