I just come to know by lots of guys that Java Applet is vulnerable.Either you have misunderstood or you were misinformed. Java applets can be a vulnerability. They aren't themselves vulnerable as far as I know.
what is the workaround for this Security issues ?Install the latest version of Java.
Can i use any RSA Certificate to prevent attacks ?Of course not. Certificates don't prevent security attacks.
Must my clients update Java to latest version on their machine ?Always.
I don't believe it's the applets that are vulnerable. It's the Java Runtime Environment (or JRE). This is what the end-user runs on their computer in order to run Java applets. If a malware author finds a security hole in the JRE then unsuspecting people who visit their malware-infected website could unknowingly run the bad applet. They can allow viruses to be installed on the end-user's computer without them ever knowing. Users should keep Java up-to-date and run a patched anti-virus. It my personally believe, move away from using Java if possible.