If the individuals qualify as your dependent, then you are entitled to claim them as such. The key condition here would be if you furnish over half of their support, and if they earn less than $4,200 (If age 19 or over). They would qualify based on the familial circumstances since they are either siblings or descendants of your sibling.
However, since your nephew already claimed the child as his dependent, you would have to mail your tax return in to do the same. If you to that, your claim will be denied and your tax refund or amount due will be adjusted. You will then have to protest that adjustment to have the matter investigated by the IRS to determine who is allowed the dependent.
It would be best if you can get your nephew to amend his return to remove the dependent claim if he is in error.
I suggest you enter the individuals into your tax return in TurboTax and answer the questions to see if he or she qualifies as your dependent.
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