Using Mockito to mock a local variable of a method

You cannot mock a local variable. What you could do, however, is extract its creation to a protected method and spy it:

public class A {
  public void methodOne(int argument) {
    //some operations
    methodTwo(int argument);
    //some operations
  }

  private void methodTwo(int argument) {
    DateTime dateTime = createDateTime();
    //use dateTime to perform some operations
  }

  protected DateTime createDateTime() {
    return new DateTime();
  }
}

public class ATest {
  @Test
  public void testMethodOne() {
    DateTime dt = new DateTime (/* some known parameters... */);
    A a = Mockito.spy(new A());
    doReturn(dt).when(a).createDateTime();
    int arg = 0; // Or some meaningful value...
    a.methodOne(arg);
    // assert the result
}