An alternative solution can be importing the module into its own code file and using the imported instance of all of the exported entities. Like this:

import * as thisModule from './module';

export function bar () {
    return 'bar';
}

export function foo () {
    return `I am foo. bar is ${thisModule.bar()}`;
}

Now mocking bar is really easy, because foo is also using the exported instance of bar:

import * as module from '../src/module';

describe('module', () => {
    it('foo', () => {
        spyOn(module, 'bar').and.returnValue('fake bar');
        expect(module.foo()).toEqual('I am foo. bar is fake bar');
    });
});

Importing the module into its own code looks strange, but due to the ES6's support for cyclic imports, it works really smoothly.

The problem seems to be related to how you expect the scope of bar to be resolved.

On one hand, in module.js you export two functions (instead of an object holding these two functions). Because of the way modules are exported the reference to the container of the exported things is exports like you mentioned it.

On the other hand, you handle your export (that you aliased module) like an object holding these functions and trying to replace one of its function (the function bar).

If you look closely at your foo implementation you are actually holding a fixed reference to the bar function.

When you think you replaced the bar function with a new one you just actually replaced the reference copy in the scope of your module.test.js

To make foo actually use another version of bar you have two possibilities :

1. In module.js export a class or an instance, holding both the foo and bar method:

   Module.js:

   export class MyModule {
     function bar () {
       return 'bar';
     }
   
     function foo () {
       return `I am foo. bar is ${this.bar()}`;
     }
   }
   

   Note the use of this keyword in the foo method.

   Module.test.js:

   import { MyModule } from '../src/module'
   
   describe('MyModule', () => {
     //System under test :
     const sut:MyModule = new MyModule();
   
     let barSpy;
   
     beforeEach(() => {
         barSpy = jest.spyOn(
             sut,
             'bar'
         ).mockImplementation(jest.fn());
     });
   
   
     afterEach(() => {
         barSpy.mockRestore();
     });
   
     it('foo', () => {
         sut.bar.mockReturnValue('fake bar');
         expect(sut.foo()).toEqual('I am foo. bar is fake bar');
     });
   });
   

2. Like you said, rewrite the global reference in the global exports container. This is not a recommended way to go as you will possibly introduce weird behaviors in other tests if you don't properly reset the exports to its initial state.

fwiw, the solution I settled on was to use dependency injection, by setting a default argument.

So I would change

export function bar () {
    return 'bar';
}

export function foo () {
    return `I am foo. bar is ${bar()}`;
}

to

export function bar () {
    return 'bar';
}

export function foo (_bar = bar) {
    return `I am foo. bar is ${_bar()}`;
}

This is not a breaking change to the API of my component, and I can easily override bar in my test by doing the following

import { foo, bar } from '../src/module';

describe('module', () => {
    it('foo', () => {
        const dummyBar = jest.fn().mockReturnValue('fake bar');
        expect(foo(dummyBar)).toEqual('I am foo. bar is fake bar');
    });
});

This has the benefit of leading to slightly nicer test code too :)