Do the children of a deceased sister, whose father has passed away and who have no provider, deserve zakat? Are they more deserving of kindness?

Zakat (definition) is given to the eight categories mentioned in the Holy Quran. If your sister's children are poor, needy, or in debt, it is permissible to give them zakat. They have a greater right to it than others, based on the Prophet's (peace and blessings be upon him) saying: "Charity given to a poor person is charity, and charity given to a relative is both charity and upholding the ties of kinship."