Need to change my verification email

If you know your password and can log in to your Apple ID, the following has instructions for changing your email addresses: Manage your Apple ID primary, rescue, alternate, and notification email addresses - Apple Support

If you don't know your password and can't use any of the methods described in If you forgot your Apple ID password - Apple Support then you will need to contact Apple account security: Contact Apple for help with Apple ID account security - Apple Support