Zakah on property for which Zakah paid previous year

Is it necessary to pay Zakah for a property (for current year), for which the Zakah is paid in the previous year? Please enclose with authentic Hadith.

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Two kinds of properties are subject to payment of Zakah:
The First requires Zakah to be paid every year such as: gold, silver, commercial commodities and "Saema" animals (cows, sheep goats and camels that have pastured by themselves, the year in the available pasture). The Zakah of this kind must be paid on yearly bases for the Hadith reported by Ibn Majah that "No Zakah is due on any commodity before it has passed a year in the hands of its owner".
The Second category of property for which Zakah must be paid include items which are weighed and stored such as grains, fruits, farm products and minerals, etc. their owner must pay the Zakah due on them as soon as their amount accumulates to the Nisaab (the amount which makes the payment of Zakah compulsory). When the owner pays the Zakah on that amount of property in this category, he is not required to pay it again no matter how long he owns it. The time period of one year does not apply to items in this category. However, if there is an increase in the amount of property for which he has paid Zakah, whenever the amount of the increase reaches the Nisaab, Zakah must be paid on the amount of the increase not matter how often it occurs.
Allah knows best.