Because your Father post deceased (died after) your grandmother, his distribution would go to his estate, and eventually to his heirs. So, if your sister and you are his only heirs (presuming he has no living spouse and you have no other siblings), and there is no Will, then you and your sister would inherit from his estate.
Someone has to represent his estate to collect the money and distribute the money to your sister and you. Note that if he died before your grandmother, then you and your sister would directly inherit from your grandmother's estate. But since he died afterward, there has to be someone who has the authority to collect the distribution from your grandmother's estate to distribute to his heirs.
Because this amount is less than $50k, it could be possible to use a small estate procedure. According to the court's website, the small estate administration is a simplified court procedure available if the person who died (the "decedent") did not have many assets. To do this you need to file a form called an "Affidavit of Voluntary Administration," also known as the "small estate affidavit."
Here is a link to the court's website for more information:
https://www.nycourts.gov/courthelp/diy/smallEstate.shtml
I hope this helps you better understand the issues.
Best regards.
Answered on Dec 28th, 2020 at 6:26 AM