Use mockReturnValue(...)

import {
  getCallingCode,
  hasSupport,
} from 'utils/countryCallingCode'

jest.mock('utils/countryCallingCode', () => ({
  getCallingCode: jest.fn(),
  hasSupport: jest.fn(),
}))

describe('...', () => {
    it('...', () => {
        getCallingCode.mockReturnValue(1)
        hasSupport.mockReturnValue(false)

        expect(...
    })

    it('...', () => {
        getCallingCode.mockReturnValue(0)
        hasSupport.mockReturnValue(true)

        expect(...
    })
})

Dealing with default export from that util:

import theUtil from 'utils/theUtil'

jest.mock('utils/theUtil', () => ({
  __esModule: true,
  default: jest.fn(),
}))

describe('...', () => {
    it('...', () => {
        theUtil.mockReturnValue('some value')

        expect(...
    })

    it('...', () => {
        theUtil.mockReturnValue('some other value')

        expect(...
    })
})

Typescript:

Use as jest.Mock. eg:

...
(getCallingCode as jest.Mock).mockReturnValue(1)
...
(theUtil as jest.Mock).mockReturnValue('some value')
...

or, more cleanly:

import theUtil from 'utils/theUtil'

jest.mock('utils/theUtil', () => ({
  __esModule: true,
  default: jest.fn(),
}))
const mockTheUtil = theUtil as jest.Mock

describe('...', () => {
    it('...', () => {
        mockTheUtil.mockReturnValue('some value')

        expect(...
    })
})