Short answer. Usually not from the System. If it paid in good faith to a dependant inferior in right, and you had not notified it of your claim before the payment, the payment discharges the System from liability. Your remedy then lies against the relative who received the money.
What the law says
If the System in good faith pays income benefit to a dependent who is inferior in right to another dependent or with whom another dependent is entitled to share, such payments shall discharge the System from liability, unless and until such other dependent notifies the System of his claim prior to the payments.
Labor Code, Article 202 — Erroneous Payment. Read the full provision →
Everything turns on when you spoke up
The article draws a hard line at the moment of payment. A claim notified prior to the payments keeps the System on the hook; a claim raised afterwards does not. That is why the single most useful thing a dependant can do is put the claim in writing early, keep the stamped copy, and follow it up — an oral enquiry at a counter leaves nothing to show. The provision also protects the System only where it acted in good faith. A payment made after it had been told of a competing claim is a different matter altogether.
What the discharge does and does not do
Read carefully, the rule discharges the System — it does not declare that the relative who was paid was entitled to the money. Your entitlement as the dependant superior in right is not extinguished by someone else having been paid; what you lose is the ability to make the System pay a second time for the same benefit. Any claim you have therefore runs against the recipient, on ordinary principles about receiving what is not due. That is a separate action, with its own evidence and its own difficulties, and it is only worth pursuing if the money can still be traced.
Rival claimants, minors and incompetents
Where the System is genuinely in doubt about who ranks first, the article empowers it to decide to whom payment should be made, following the regulations the Commission approves. So the correct move when you learn that a relative is claiming is not to wait and see, but to file your own claim and let the System resolve the rivalry before money moves. The same article deals with beneficiaries who cannot manage funds: where the benefit is payable to a minor or an incompetent, the System pays the person it considers best qualified to take care of and dispose of the property for that beneficiary's benefit.
Practical steps if payment has already gone out
Ask in writing for the record: when the claim was filed, who was named, and on what date payment was released. That fixes whether your own notice came before or after. If it came before, the discharge does not apply and the System's determination can be contested through the channels its rules provide. If it came after, gather proof of your relationship and dependency anyway — it is the foundation of any claim against the recipient. Do not sign a quitclaim or a waiver in exchange for a partial payment until you understand what you are giving up.