Thanks jaikiran

I set my logging properties for the handler in the standalone-full.xml

  <profile>

        <subsystem xmlns="urn:jboss:domain:logging:3.0">

...

            <console-handler name="MY-CONSOLE" autoflush="true">

                <formatter>

                    <named-formatter name="MY-PATTERN"/>

                </formatter>

                <target name="System.out"/>

            </console-handler>

...

            <logger category="org.america3" use-parent-handlers="false">

                <level name="INFO"/>

                <handlers>

                    <handler name="WSTEST"/>

                </handlers>

            </logger>

...

            <formatter name="MY-PATTERN">

                <pattern-formatter pattern="MeMeMe%s%n"/>

            </formatter>

Here is the code in my classes used to log

FROM Member.java

     //constructors

    public Member() {

       System.out.println("\n************************ Member: System.out from Constructor");

      logger.info("************************ Member: Logged from Constructor");

FROM WSEndpoint

    @OnOpen

    public void open(Session session) {

      System.out.println("\n************************ WSEndpoint: System.out from OnOpen");

      logger.info("************************ WSEndpoint: Logged from OnOpen");

    }

Which should be called when the HTML script instatiates a new socket with

    var socketURL = "ws://localhost:8080/WSTest/WSTestSocket";

    function openUp (){

       if (!appsocket) {

          alert("Opening: appsocket " + socketURL);

         appsocket = new WebSocket(socketURL);

         alert("appsocket open: " + appsocket); **** This returns [object:Websocket]]

And this is what wildfly's log shows when it is started and deploys my EAR app:

    The Name and Member entities are clearly logging to the console. See "MeMeMe"

    And System.out is also logging to the console

10:46:40,763 INFO  [stdout] (ServerService Thread Pool -- 66)

10:46:40,764 INFO  [stdout] (ServerService Thread Pool -- 66) ************************ Member: System.out from Constructor

MeMeMe************************ Member: Logged from Constructor

10:46:40,796 INFO  [stdout] (ServerService Thread Pool -- 66)

10:46:40,796 INFO  [stdout] (ServerService Thread Pool -- 66) ************************ Name: System.out from Constructor

MeMeMe************************ Name: Logged from Constructor

But nothing is showing up from WSEndpoint.java

Hope you can suggest somewhere else to look.

This is killing me

Cudos to  jaikiran

Based on your hints I found I was right. 

It was a dumb error that had nothing to do with logging..

The Ear had two modules:

WSTest.jar that deployed the Session Beans and

WSTest.war that deployed the HTML and script files,

And I had the socket class in WSTest.jar with the Session Beans.

I'm not sure if this is the only solution, but based on your suggestions I moved the socket to WSTest.war's META-INF/classes folder.

.

And all worked.

I wish I knew how to use the forum better.

But since this is under your reply, can I  check you comment with Correct Answer to see that you get credit?  You were the only programmer who helped,and I appreciate it.