Resolution:
The values specified for Partner Serial Number and Partner Issuer CA when defining a partner depending on how the client is authenticated.

Two-way SSL (Apache HTTP Server).

Partner Serial Number - Subject DN from client's x.509 certificate.
Partner Issuer CA - Issuer DN from client's x.509 certificate.

Two-way SSL (FacadeHTTPSSLChannel).

Partner Serial Number - Serial Number(string after 0x) from client's x.509 certificate.
Partner Issuer CA - Issuer DN from client's x.509 certificate.
Note: The Serial Number configured is case-sensitive.

Basic Authentication (Apache HTTP Server)

Partner Serial Number - username
Partner Issuer CA - O=TIBCO;CN=ASG;CN=HTTP;CN=Basic Domain

Basic/UsernameToken Authentication (Security Policy)

Partner Serial Number - authenticated user's LDAP DN
Partner Issuer CA - urn:www.tibco.com

File-based Authentication (Security Policy).

Partner Serial Number - username
Partner Issuer CA - urn:www.tibco.com

Determining the values to be set for "Partner Serial Number and ‘Partner Issuer CA" when defining Partners in TIBCO API Exchange Gateway (APIX).