Chin, have you seen this askf5 solution Troubleshooting client certificate authentication, does this help?
Bear in mind that if your backend server is still expecting SSL traffic and client authentication then you will need to modify your server SSL profile too with a certificate. See Overview of the Server SSL profile.
The Certificate setting is optional. The default value for this setting is None. When you apply a Server SSL profile to a virtual server, the BIG-IP system acts as an SSL client. If you do not intend for the BIG-IP system to present its client certificate on behalf of clients traversing the virtual server, select None. If you expect the BIG-IP system to present a client certificate, import the certificate and matching key to the BIG-IP system, and then choose the appropriate certificate from the menu.
Hope this helps,
N