Controlling Signup button functionality
Currently there is no support to disable Signup functionality. If we disable Identities, it disables the Login also.
There must be a way to achieve this. Refer below link for more details:
As a workaround you can assign your "API products" to users groups by using "Access control" on "API products".
Users can still "sign up" but they don't see any API or product on the portal until you move them user to the correct user(s) group(s). Even better, users don't see all APIs but only those authorized for their group.