Need to write Irule to decode auth string to Base64 and fetch domain name from it and compare that domain name with certificate to deny/permit traffic

Try this:

when HTTP_REQUEST {
    if { [HTTP::header exists Authorization] } {
        catch { 
            set creds [b64decode [findstr [HTTP::header Authorization] "Basic " 6]]

             credentials will ether be in domain\user:password or user@domain:password format
            if { $creds contains "\\" } {
                set domain [findstr $creds "" 0 "\\"]
            } elseif { $creds contains "@" } {
                set domain [findstr $creds "@" 1 ":"]
            }

            log local0. $domain
        }
    }
}

Once you have the domain value you can simply apply logic to compare it to the certificate:

if { $domain ne "" } {
    if { $domain eq $cert_valu } {
         ...do something
    }
}