There is a possibility in applet code to trigger client authentication dialog to popup, but it fails due to following exception. (Test case attached)

java.security.AccessControlException: access denied (java.lang.RuntimePermission modifyThreadGroup)
at java.security.AccessControlContext.checkPermission(Unknown Source)
at java.security.AccessController.checkPermission(Unknown Source)
at java.lang.SecurityManager.checkPermission(Unknown Source)
at sun.applet.AppletSecurity.checkAccess(Unknown Source)
at java.lang.ThreadGroup.checkAccess(Unknown Source)
at java.lang.Thread.init(Unknown Source)
at java.lang.Thread.<init>(Unknown Source)
at sun.plugin.util.PluginSysUtil$SysExecutionThread.<init>(Unknown Source)
at sun.plugin.util.PluginSysUtil.execute(Unknown Source)
at sun.plugin.util.PluginSysUtil.delegate(Unknown Source)
at com.sun.deploy.util.DeploySysRun.execute(Unknown Source)
at com.sun.deploy.security.X509DeployKeyManager.chooseClientAlias(Unknown Source)
at com.sun.net.ssl.internal.ssl.JsseX509KeyManager$AbstractWrapper.chooseClientAlias(Unknown Source)
at com.sun.net.ssl.internal.ssl.JsseX509KeyManager.chooseClientAlias(Unknown Source)
at com.sun.net.ssl.internal.ssl.ClientHandshaker.serverHelloDone(Unknown Source)
at com.sun.net.ssl.internal.ssl.ClientHandshaker.processMessage(Unknown Source)
at com.sun.net.ssl.internal.ssl.Handshaker.processLoop(Unknown Source)
at com.sun.net.ssl.internal.ssl.Handshaker.process_record(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.readRecord(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.performInitialHandshake(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.startHandshake(Unknown Source)
at sun.net.www.protocol.https.HttpsClient.afterConnect(Unknown Source)
at sun.net.www.protocol.https.AbstractDelegateHttpsURLConnection.connect(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection.getInputStream(Unknown Source)
at sun.net.www.protocol.https.HttpsURLConnectionImpl.getInputStream(Unknown Source)
at HttpsTest.start(HttpsTest.java:16)
at sun.applet.AppletPanel.run(Unknown Source)
at java.lang.Thread.run(Unknown Source)
java.net.SocketException: Software caused connection abort: recv failed
at java.net.SocketInputStream.socketRead0(Native Method)
at java.net.SocketInputStream.read(Unknown Source)
at com.sun.net.ssl.internal.ssl.InputRecord.readFully(Unknown Source)
at com.sun.net.ssl.internal.ssl.InputRecord.read(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.readRecord(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.waitForClose(Unknown Source)
at com.sun.net.ssl.internal.ssl.HandshakeOutStream.flush(Unknown Source)
at com.sun.net.ssl.internal.ssl.Handshaker.sendChangeCipherSpec(Unknown Source)
at com.sun.net.ssl.internal.ssl.ClientHandshaker.sendChangeCipherAndFinish(Unknown Source)
at com.sun.net.ssl.internal.ssl.ClientHandshaker.serverHelloDone(Unknown Source)
at com.sun.net.ssl.internal.ssl.ClientHandshaker.processMessage(Unknown Source)
at com.sun.net.ssl.internal.ssl.Handshaker.processLoop(Unknown Source)
at com.sun.net.ssl.internal.ssl.Handshaker.process_record(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.readRecord(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.performInitialHandshake(Unknown Source)
at com.sun.net.ssl.internal.ssl.SSLSocketImpl.startHandshake(Unknown Source)
at sun.net.www.protocol.https.HttpsClient.afterConnect(Unknown Source)
at sun.net.www.protocol.https.AbstractDelegateHttpsURLConnection.connect(Unknown Source)
at sun.net.www.protocol.http.HttpURLConnection.getInputStream(Unknown Source)
at sun.net.www.protocol.https.HttpsURLConnectionImpl.getInputStream(Unknown Source)
at HttpsTest.start(HttpsTest.java:16)
at sun.applet.AppletPanel.run(Unknown Source)
at java.lang.Thread.run(Unknown Source)