Try this

index.test.js

const mockFs = {
  createReadStream: function () {
    return this;
  },
  mkdir: function (p, cb) {
    cb(null, this);
  },
  pipe: function () {
    return this;
  },
  on: function (param, cb) {
    if (param === 'close') {
      return cb();
    }
    if (param === 'error') {
      return this;
    }
  },
};

ava.serial('unZip success', async (t) => {
  const unzip = proxyquire('../../../src/helpers/file/unZip', {
    fs: mockFs,
    util: {},
    unzipper: { Extract: () => Buffer.from([8, 6, 7, 5, 3, 0, 9]) },
  });
  const mockZipFilePath = '../file/testFile.txt';
  const destinationFilePath = '../file';

  const result = await unzip(mockZipFilePath, destinationFilePath);

  t.is(result, destinationFilePath);
});

I am new to ava so may be it's wrong

proxyquire('../../../src/helpers/file/unZip')// actual function file

ava('69616649', () => {
  ava.afterEach(() => {
    sinon.restore();
  });
  ava.serial('should pass', async () => {
    sinon.stub(fs, 'mkdir').callsFake((path, callback) => {
      callback();
    });
    const rs = {
      pipe: sinon.stub().returnsThis(),
      on: sinon.stub().callsFake(function (event, callback) {
        if (event === 'close') {
          callback();
        }
      }),
    };
    sinon.stub(fs, 'createReadStream').returns(rs);
    sinon.stub(unzipper, 'Extract');
    const actual = await unZip('fakeFileContent', 'fakeFileContent');
    sinon.assert.match(actual, 'fakeFileContent');
    sinon.assert.calledWithExactly(
      fs.mkdir,
      'fakeFileContent',
      sinon.match.func
    );
    sinon.assert.calledWithExactly(fs.createReadStream, 'fakeFileContent');
    sinon.assert.calledWithExactly(unzipper.Extract, {
      path: 'fakeFileContent',
    });
    sinon.assert.calledOnce(rs.pipe);
    sinon.assert.calledWithExactly(rs.on, 'close', sinon.match.func);
  });
});

You don't need to use proxyquire package, use sinon.stub(obj, 'method') to stub methods of object. You can stub fs.mkdir, unzipper.Extract and fs.createReadStream methods.

You use util.promisify to convert fs.mkdir into a promise form and call it, but underly is still the callback being called, so you need to use the .callsFake() method to mock implementation for fs.mkdir, and call the callback manually in the test case.

The below example uses mocha as testing framework, but ava should also be fine.

index.js:

const fs = require('fs');
const util = require('util');
const unzipper = require('unzipper');

const unZip = async (zipFilePath, destDir) => {
  await util.promisify(fs.mkdir)(destDir);

  return new Promise((resolve, reject) => {
    fs.createReadStream(zipFilePath)
      .pipe(unzipper.Extract({ path: destDir }))
      .on('close', () => resolve(destDir))
      .on('error', (err) => {
        console.log('Error inside unzip', err);
        reject(err);
      });
  });
};

module.exports = unZip;

index.test.js:

const unZip = require('./');
const fs = require('fs');
const sinon = require('sinon');
const unzipper = require('unzipper');

describe('69616649', () => {
  afterEach(() => {
    sinon.restore();
  });
  it('should pass', async () => {
    sinon.stub(fs, 'mkdir').callsFake((path, callback) => {
      callback();
    });
    const rs = {
      pipe: sinon.stub().returnsThis(),
      on: sinon.stub().callsFake(function (event, callback) {
        if (event === 'close') {
          callback();
        }
      }),
    };
    sinon.stub(fs, 'createReadStream').returns(rs);
    sinon.stub(unzipper, 'Extract');
    const actual = await unZip('fakeFileContent', 'fakeFileContent');
    sinon.assert.match(actual, 'fakeFileContent');
    sinon.assert.calledWithExactly(fs.mkdir, 'fakeFileContent', sinon.match.func);
    sinon.assert.calledWithExactly(fs.createReadStream, 'fakeFileContent');
    sinon.assert.calledWithExactly(unzipper.Extract, { path: 'fakeFileContent' });
    sinon.assert.calledOnce(rs.pipe);
    sinon.assert.calledWithExactly(rs.on, 'close', sinon.match.func);
  });
});

test result:

  69616649
    ✓ should pass


  1 passing (7ms)

----------|---------|----------|---------|---------|-------------------
File      | % Stmts | % Branch | % Funcs | % Lines | Uncovered Line #s 
----------|---------|----------|---------|---------|-------------------
All files |   81.82 |      100 |      75 |   81.82 |                   
 index.js |   81.82 |      100 |      75 |   81.82 | 13-14             
----------|---------|----------|---------|---------|-------------------