How to test void method with private method calls using Mockito

If you really want to verify it, you need to change your A class and extract the super call into a private method:

public class A extends B {

    private boolean workDone = false;

    @Override
    public void publicMethod(final boolean flag) {
        if (!workDone) {
            privateMethod();
            workDone = true;
        }
        callParentPublicMethod(flag);
    }

    private void callParentPublicMethod(final boolean flag) {
        super.publicMethod(flag);
    }

    private void privateMethod() {
        System.out.println("A: privateMethodCalled");
    }
}

after this is done you can use PowerMock to verify private method invocations:

  import org.junit.Test;
import org.junit.runner.RunWith;
import org.powermock.api.mockito.PowerMockito;
import org.powermock.core.classloader.annotations.PrepareForTest;
import org.powermock.modules.junit4.PowerMockRunner;

@RunWith(PowerMockRunner.class)
@PrepareForTest({ A.class })
public class ATest {

    @Test
    public void publicMethod_test_false() throws Exception {

        A spy = PowerMockito.spy(new A());
        spy.publicMethod(false);
        PowerMockito.verifyPrivate(spy).invoke("privateMethod");
        PowerMockito.verifyPrivate(spy).invoke("callParentPublicMethod", false);
    }

    @Test
    public void publicMethod_test_true() throws Exception {

        A spy = PowerMockito.spy(new A());
        spy.publicMethod(true);
        PowerMockito.verifyPrivate(spy).invoke("privateMethod");
        PowerMockito.verifyPrivate(spy).invoke("callParentPublicMethod", true);
    }
}

Hope this helps.