You didn't specify, but I'm assuming your ASP site is a local intranet site that's connecting to a hosted Azure SQL database. If so, make sure you are using the latest driver for provider. See https://www.sqlnethub.com/blog/dbnetlib-connectionopen-secdoclienthandshake-ssl-security-error-resolve/, it's a blog post that details where to find the latest drivers and how to enable the TLS version on your local machine.
Regards,
Ryan