Can a dependent who is a qualifying relative because of age qualify for Earned Income Credit if they have qualifying child?

A dependent cannot HAVE a dependent.

The question is about EIC where qualifying child for EIC doesn't have to be your dependent.

The *only* case where the child does not have to be your dependent is in the case of divorced or separated parents that live apart.    Then the child *would* have been your dependent but is not because yiu are allowing the non-custodial parent to claim instead.   Does not apply if you *are* yourself a dependent, since the child could not have been your dependent at all.

Publication 596 page 13 examples 1 and 2 point out that dependent status is not in the four tests for qualifying child for earned income credit, and the taxpayer dependent status is not relevant to qualifying for earned income credit.

What boxes do I check to claim the earned income credit given the IRS examples?

Publication 596, Page 13
Example 1—child lived with parent and grandparent. You and your 2-year-old son Jimmy lived with your mother all year. You are 25 years old, unmarried, and your AGI is $9,000. Your only income was $9,000 from a part-time job. Your mother's only income was $20,000 from her job, and her AGI is $20,000. Jimmy's father did not live with you or Jimmy. The special rule explained later for divorced or separated parents (or parents who live apart) doesn't apply. Jimmy is a qualifying child of both you and your mother because he meets the relationship, age, residency, and joint return tests for both you and your mother. However, only one of you can treat him as a qualifying child to claim the EIC (and the other tax benefits listed earlier in this chapter for which that person qualifies). He isn't a qualifying child of anyone else, including his father. If you don't claim Jimmy as a qualifying child for the EIC or any of the other tax benefits listed earlier, your mother can treat him as a qualifying child to claim the EIC (and any of the other tax benefits listed earlier for which she qualifies).

Example 2—parent has higher AGI than grandparent. The facts are the same as in Example 1 except your AGI is $25,000. Because your mother's AGI isn't higher than yours, she cannot claim Jimmy as a qualifying child. Only you can claim him.

You are missing that to clam the credit, you must first be able to treat (claim) the child as a *Qualifying Child*.  

You cannot do that because a dependent cannot have a dependent - see the requirements for a "Qualifying Child".  A Qualifying Child is what make the child a dependent.  If the child is not a Qualifying Child (dependent) you cannot claim the EIC or any other credits.

 "However, only one of you can treat him as a *qualifying child* to claim the EIC"

But the tests for qualifying child for earned income credit are relationship, age, joint return and residency.  There is no requirement that a child qualifying for earned income credit be your dependent.  There is no such rule.  It is not the child tax credit.

What boxes do I check to take the earned income credit?

See rule #12 in that same Publication on page 16.

There is not box, since a dependent cannot claim that credit.

There are no boxes you can check, because you don't qualify.
When you start the EIC interview in TT, you will be told you don't qualify because you can be claimed as a dependent and your child(ren) doesn't qualify.
When you click "why does this matter", you get this explanation:
Each credit has its own rules, and one of the Earned Income Credit's rules is: If you can be someone's dependent, you can't get this credit.The thinking is that if someone supports you, then that person could get this credit instead of you.
When you click "learn more", you get this explanation:
Based on what you told us earlier, it turns out you have a dependent who doesn't count as a qualifying child for the earned income credit (EIC).

Rule 12 only applies if you don't have a child that meets the relationship, age, residency and joint return test.  TurboTax claims I "have a dependent who doesn't count as a qualifying child for the earned income credit (EIC)" which is an incorrect statement because the children meet the four tests for qualifying children for EIC.  Unlike child tax credit, a qualifying child for the earned income credit does not have to be your dependent.  That's why I'm here.

What boxes do I check to take the earned income credit?

As others have said, your father cannot claim you as a either a qualifying child or qualifying relative dependent. If somehow he could (e.g. your taxable income was less than $4000), you would not be allowed to claim a qualifying child of your own (a dependent can not have a dependent). You are also not allowed to claim EIC based on children who are not your dependents. There are a couple of exceptions (described in the comments), but they don't apply to your situation.

If you and your children live with your father, he can claim one or more of your children as HIS qualifying child.

I was mistaken, I only made $3,000.  My father's earned income is too high to claim the earned income credit.  What boxes do I check to claim the earned income credit while being a dependent on another return?

You can't. A dependent is not allowed to claim the EITC. A dependent is also not allowed to claim a dependent of her own.
Here's more bad news: it's not optional. If you qualify as you father's dependent, you may not claim your own exemption, dependents or EITC even if he doesn't actually claim you.

But the tests for qualifying child for earned income credit are relationship, age, joint return and residency.  There is no requirement that a child qualifying for earned income credit be your dependent.  There is no such rule.  It is not the child tax credit.

What boxes do I check to take the earned income credit?

There is such a rule (that the child must be your dependent). There are a couple of exceptions, which may be leading you astray; as you don't qualify for either:
1. the previously mentioned divorced parents special rule
2. if the child is not a dependent only because he provided more than half his own support, he still qualifies the parent (taxpayer) for EIC.
The only box in TT that you can check, to get the EIC, is the one that says you can't be claimed as a dependent.  But, as previously explained, that's not allowed. So, that would be tax fraud. The IRS is particularly tough on EIC tax fraud.

BTW, the EIC for someone with $3000 of income and 3 kids is $1361.
For a grandfather who makes too much to claim EIC, the tax savings from  claiming 3 more kids just as dependents is a least $3000 and could be more, much more

That's the point.  Grandfather can claim myself and all the children for dependents, and I can claim EIC because there is no support requirement and the qualifying children for EIC don't have to be dependents, just meet relationship, age, residency, and joint return tests.  Grandfather gets dependents, mother gets EIC.

What boxes do I check to take the earned income credit?

Publication 596, Page 11, Rule 9:

Sometimes a child meets the tests to be a qualifying child of more than one person. However, only one of these persons can actually treat the child as a qualifying child. Only that person can use the child as a qualifying child to take all of the following tax benefits (provided the person is eligible for each benefit).

The exemption for the child.
The child tax credit.
Head of household filing status.
The credit for child and dependent care expenses.
The exclusion for dependent care benefits.
The EIC.

The other person cannot take any of these benefits based on this qualifying child. In other words, you and the other person cannot agree to divide these tax benefits between you. The other person cannot take any of these tax benefits unless he or she has a different qualifying child.

You cannot be your father's dependent since (1) you are 24 or over and (2) you had income in excess of $4,000.

I was mistaken, I only made $3,000.  What boxes do I check to claim the earned income credit?