Scenario 1. If the super class does not declare an exception:

1.1 The sub class declares a checked exception

class SuperClass {
    void foo() {

    }
}

import java.io.IOException;
class SubClass extends SuperClass {
    @Override
    void foo() throws IOException {

    }
}

// overridden method does not throw 'java.io.IOException'

1.1 The sub class declares a unchecked exception

class SuperClass {
    void foo() {

    }
}

class SubClass extends SuperClass {
    @Override
    void foo() throws ArithmeticException  {

    }
}

// Okay

Scenario 2. If the super class declares an exception:

2.1 The sub class declares a exception other than the child exception of the super class exception

class SuperClass {
    void foo() throws RuntimeException {

    }
}

import java.io.IOException;

class SubClass extends SuperClass {
    @Override
    void foo() throws IOException {

    }
}

// overridden method does not throw 'java.io.IOException'

2.2 The sub class declares a child exception of the super class exception

class SuperClass {
    void foo() throws RuntimeException {

    }
}

class SubClass extends SuperClass {
    @Override
    void foo() throws ArithmeticException {

    }
}

// Okay

2.3 The sub class does not declare exception

class SuperClass {
    void foo() throws RuntimeException {

    }
}

class SubClass extends SuperClass {
    @Override
    void foo() {

    }
}

// Okay

2.4 The sub class declares an unchecked exception

import java.io.IOException;

class SuperClass {
    void foo() throws IOException {
        System.out.println("This is in super class.");
    }
}

class SubClass extends SuperClass {
    @Override
    void foo() throws ArithmeticException{
        System.out.println("This is in sub class.");
    }
}

// Okay

Conclusion:

• If Super Class does not declare an exception, then the Sub Class can only declare unchecked exceptions, but not the checked exceptions.
• If SuperClass declares an exception, then the SubClass can only declare the child exceptions of the exception declared by the SuperClass, but not any other exception. Except the following scenario:
• If SuperClass declares a checked exception, the SubClass can declare an unchecked exception.
• If SuperClass declares an exception, then the SubClass can declare without exception.