Is it good practice to use ordinal of enum?

First, you probably don't even need a numeric order value -- that's what Comparable is for, and Enum<E> implements Comparable<E>.

If you do need a numeric order value for some reason, yes, you should use ordinal(). That's what it's for.

Standard practice for Java Enums is to sort by declaration order, which is why Enum<E> implements Comparable<E> and why Enum.compareTo() is final.

If you add your own non-standard comparison code that doesn't use Comparable and doesn't depend on the declaration order, you're just going to confuse anyone else who tries to use your code, including your own future self. No one is going to expect that code to exist; they're going to expect Enum to be Enum.

If the custom order doesn't match the declaration order, anyone looking at the declaration is going to be confused. If it does (happen to, at this moment) match the declaration order, anyone looking at it is going to come to expect that, and they're going to get a nasty shock when at some future date it doesn't. (If you write code (or tests) to ensure that the custom order matches the declaration order, you're just reinforcing how unnecessary it is.)

If you add your own order value, you're creating maintenance headaches for yourself:

1. you need to make sure your hierarchy values are unique
2. if you add a value in the middle, you need to renumber all subsequent values

If you're worried someone could change the order accidentally in the future, write a unit test that checks the order.

In sum, in the immortal words of Item 47: know and use the libraries.

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P.S. Also, don't use Integer when you mean int. 🙂

As suggested by Joshua Bloch in Effective Java, it's not a good idea to derive a value associated with an enum from its ordinal, because changes to the ordering of the enum values might break the logic you encoded.

The second approach you mention follows exactly what the author proposes, which is storing the value in a separate field.

I would say that the alternative you suggested is definitely better because it is more extendable and maintainable, as you are decoupling the ordering of the enum values and the notion of hierarchy.

The first way is not straight understandable as you have to read the code where the enums are used to understand that the order of the enum matters.
It is very error prone.

public enum Persons {

    CHILD,
    PARENT,
    GRANDPARENT;

}

The second way is better as it is self explanatory :

CHILD(0),
PARENT(1),
GRANDPARENT(2);

private SourceType(final Integer hierarchy) {
    this.hierarchy = hierarchy;
}

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Of course, orders of the enum values should be consistent with the hierarchical order provided by the enum constructor arguments.

It introduces a kind of redundancy as both the enum values and the arguments of the enum constructor conveys the hierarchy of them.
But why would it be a problem ?
Enums are designed to represent constant and not frequently changing values.
The OP enum usage illustrates well a good enum usage :

CHILD, PARENT, GRANDPARENT

Enums are not designed to represent values that moves frequently.
In this case, using enums is probably not the best choice as it may breaks frequently the client code that uses it and besides it forces to recompile, repackage and redeploy the application at each time an enum value is modified.

TLDR: No, you should not!

If you refer to the javadoc for ordinal method in Enum.java:

Most programmers will have no use for this method. It is designed for use by sophisticated enum-based data structures, such as java.util.EnumSet and java.util.EnumMap.

Firstly - read the manual (javadoc in this case).

Secondly - don't write brittle code. The enum values may change in future and your second code example is much more clear and maintainable.

You definitely don't want to create problems for the future if a new enum value is (say) inserted between PARENT and GRANDPARENT.