I've two classes Parent and Child.

class Child extends Parent {
    private String extraField1;
    private String extraField2;
    ...
}

Child class has 2 extra fields extraField1 and extraField2.

Q1. Must I make two diff. tables within the databse: one for Child along with other for Parent?

or

Q1. Must I add two posts within the Parent table (each column for just one extra area) and keep Child within the Parent table.

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Yes, Child and Parent are classes within the same hierarchy.

If there is 2 datatables for any Parent and Child class in Java?

There's no universal response to this. You will find really several strategies to map an inheritance hierarchy right into a relational database and every one has pros and cons. Selecting either is dependent in your context.

Scott Ambler particulars the different approaches within the section 2. Mapping Inheritance Structures of his famous paper Mapping Objects to Relational Databases: O/R Mapping In Detail that I am estimating below:

(...) Within this section you will see that you will find three primary solutions for mapping inheritance right into a relational database, along with a 4th extra technique that goes past inheritance mapping. They are:

For any full comparison (with advantages, disadvantages along with a recommendation on when you should use), take a look in the section 2.6 Comparing The Strategies.

I can not perform a better job than him so there's no reason at paraphrasing him, just make reference to the initial paper.