Can I have financial claim on someone whom I took care and recently died?

In Georgia, no. To have a claim he either had to name you in his will or you had to have a written contract.

You can make the claim. The family is going to say the services were gratuitous. There are deadlines for making a claim in an estate, so if you're going to do it, do it soon.

You have a right to file a claim against his estate. The personal representative may not object to the claim but depending on the size of the estate compared to the amount of the claim, the larger the claim, in relation to the value of the estate and the relationship which you have with his relatives, the more likely an objection will be filed. The problem you have is that he did not pay you for care and you have no contractual right to pay. Your question suggests that you did it out of friendship, not for pay. You may be able to claim for out of pocket costs you incurred if you can supply proper documentation showing dates, amounts and the relationship to his care. Generally, I would say that you are facing an uphill battle.

It would be very difficult to successfully make such a claim unless there was an agreement that he would pay you.

Making a claim against an estate for in-home care of a friend or loved one can be difficult. The truth is that many times these claims often fall under the category of "things that you would have done anyway." Effectively, you are taking the position of being a creditor owed a debt by the estate for the services that you provided. As with any creditor's claim, much of the viability is found in the details. Was there an agreement of some kind between you and the decedent, verbal, or in writing? Was there an expectation of remuneration on your part and expectation of payment for the services on the decedent's part? Is it possible to prove a debt and recover a part of the estate for your services? Sure. Whether or not it is likely depends far too much on the specific arrangement. Your best bet is to consult with a probate attorney near you to outline all of the relevant facts involved.