A.js

module.exports = Alloy.getController('BaseController').extend({
    customFunction: function(){ alert('inherited function call!'); }
});

B.js

module.exports = Alloy.getController('A').extend({
    preLayout: function(args) { // OPTIONAL
        // do stuff before the view hierarchy is created, like update styles with runtime values
        // or execute the parent controller's constructor
        // Alloy.getController('A').call(this, args);
    },
    postLayout: function(args) { // OPTIONAL
        // do stuff after the view hierarchy is created
    }
});

index.js

module.exports = Alloy.getController('BaseController').extend({
    postLayout: function(args) {
        var B = Alloy.getController('B');
        var instance = new B(); 

        instance.customFunction(); // makes function call defined in A.js
    }
});