HTTPS Monitor

Is the server corresponding to your pool member requiring certificate based authentication for incoming connections? If so, you can specify a certificate and key in the HTTPS monitor to use to authenticate the LTM. If not, then the LTM won't be presenting a certificate; only the server will.

If its a basic HTTPS monitor which tests TCP 443 reachability, certs doesn't matter. Certificate handshake will come into picture if you are using an advanced monitor where you access traffic thru TCP 443.

unless your server ask for certificate based authentication , you no need to worry about https monitor. If it required , you need to configure cert and key in monitor

Which Cert I need to configure (Self cert in client tab in f5) ?????

it can be anyone which is approved by your CA.

Which Cert I need to configure (Self cert in client tab in f5) ?????

it is client certificate which server requests during ssl handshake.

this is article about client certificate authentication (Client Authentication and How Does Client Authentication Work sections).

SSL Profiles Part 8: Client Authentication by John Wagnon

Thanks to Everyone sharing thoughts and good explanation. @Nitass...i have another question By default client cert option is select ignore in BIGIP. Like same We can need to do in server side (Because BIGIP is client for server when it is making a secure connection with bigip in offload time). am i right ??????? If Server is asking for client auth while making a connection from BIGIP to server side when Cert bigip will present to server.....Is it self sign cert ????????What happened if BIGIP and Server have same cert (How communication will happen between them)

By default client cert option is select ignore in BIGIP. Like same We can need to do in server side (Because BIGIP is client for server when it is making a secure connection with bigip in offload time). am i right ?

yes

If Server is asking for client auth while making a connection from BIGIP to server side when Cert bigip will present to server.....Is it self sign cert ?

server is the one who verifies certificate bigip (serverssl) provides. if server accepts self-signed certificate, yes you can use self-signed certificate in serverssl profile.