The initialScreen parameter is a parameter used with Lock (within the customised hosted login page at Auth0) , not as parameter with the auth0.js authorize call.
See examples
According to the documentation you can pass custom parameters .
Have in mind that the parameters are sent by the client application so the end-user can modify them and as such, in general, you should not make any security decision based on them. For your specific scenario the parameter is used just to influence the default UI shown so the above does not apply as it has no security implications.
From the webAuth.authorize depending on the user intentions you would pass a conditional parameter:
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Hello,
I wonder how can I redirect user to hosted signup page ( I know It’s same as login page but signup tab should be shown insted of login ) ?
Thank you.