Is this possible to design a function which takes a parameter and returns an object which holds multiple properties or functions

You can't use an arrow function as a constructor, so tyou could change your code to use a traditional function:

function objectName(userName)  {
  var rowCount = 0;
  init = function() {
    // make call to server and read data
    rowCount = 5; // setting dummy data
  };

  this.fetchNext = function(){
       // logic here
       const resultList = [] // new data
       return resultList;
  };

  
  init();
};

var myObj = new objectName("foo");
console.log(myObj.fetchNext());

Or, you can return an object from your arrow function

var objectName = (userName) => {
  var rowCount = 0;
  function init() {
    // make call to server and read data
    rowCount = 5; // setting dummy data
  };

  
  
  init();
  
  return {
    fetchNext: function(){
       // logic here
       const resultList = [] // new data
       return resultList;
    }

  }
};

var myObj = objectName("Foo");
console.log(myObj.fetchNext());

Related:

  • Are 'Arrow Functions' and 'Functions' equivalent / interchangeable?

For completeness, the reason your edit did not work is that you defined x but never executed the function. This works:

var x = function(){
    var a = function(){console.log('a');};
    var b = function(){console.log('b');};
    return {a: a, b: b};
}
x().a(); // must execute x to get the result

And is esssentially the same as my second example above