Is it permissible to count the amount paid to help those in need —who are eligible to receive Zakat— as part of the Zakat before the year is due, and to roll over the remaining amount for the following year’s Zakat? And does this count as stinginess and contradict the Hadith: "There is a right in wealth other than Zakat"?

It is permissible to count the amount sent to the Zakat (definition) fund from the Zakat of the coming year or the year after, because it is permissible to pay Zakat in advance for two years or less. As for whether there is a right other than Zakat in wealth, scholars have differed on this. Voluntary charity increases good deeds and indicates generosity of spirit and the absence of stinginess, and Allah Almighty says: "And whoever is protected from the stinginess of his soul - it is those who will be the successful."