You will need to login to your account through TurboTax online in order to change your account information.
Changing your email address yourself saves time. Here's how to do it:
If you no longer have access to your email address and are unable to login to your TurboTax Online account, please complete the Account Recovery Request Submission Form.
Related Information:
Source: TurboTax FAQ
I have followed he steps provided to change my email address however it continues to ask me to verify my account
You can have the verification code texted to your mobile phone if you no longer have access to your email. Please see How do I get a verification code if the email address is wrong? for instructions.