Answer
Wa `alaykum as-Salamuwa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If the money you receive reaches the nisab and a lunar year passed while possessing it, then the money is subject to Zakah.
Answering your question, the Fatwa Center at Islam Q and A, states:
Firstly:
Zakah is due on cash if you have full possession of the nisab (minimum threshold) and one full hijri year has passed.
The expenses that a father gives to his son is something that the son takes full possession of and disposes of as he wishes, so that is subject to Zakah.
Secondly:
It is well known that cash in the form of bank notes was not known at the time of the Prophet (peace and blessings be upon him), but the scholars have ruled that it is subject to Zakah by analogy with gold and silver.
The nisab for gold is 85 grams, and the nisab for silver is 595 grams.
If the cash reaches the value of the nisab for gold or silver, then it has reached the minimum threshold.
As silver is of a lower price nowadays, the nisab for cash may be worked out on the basis of the nisab for silver, because that is more on the safe side and is more beneficial to the poor.
Based on the price of silver nowadays, the nisab for cash is approximately 1093 Saudi Riyals. If you own this amount of money and one full lunar (hijri) year has passed since you acquired this amount and it has not dipped below the nisab during this year, then Zakah must be paid on it, at a rate of 2.5 %.
But if the cash you possessed is less than the nisab during the year, then Zakah does not have to be paid on it until it reaches the nisab again and you start to reckon a new year from the time it reached the nisab.
If the amount by which it dipped below the nisab was small, then in order to be on the safe side you may pay Zakah, and carry on counting the year. That is because the price of silver fluctuates and does not remain constant throughout the year.
We should not forget to commend your keenness and concern with regard to Zakah, even though you are talking about pocket money that you take from your father, but you are paying attention to Allah’s right in it and have asked about the Islamic ruling on it at a time when many rich people neglect this pillar of Islam and do not acknowledge Allah’s rights over their wealth or spend a lot or a little of it, and they spend their days accumulating and hoarding and seeking to acquire more, but at the reckoning on the Day of Resurrection their wealth will be a cause of loss and regret.
Allah Almighty says,
{And those who hoard up gold and silver (Al‑Kanz: the money, the Zakah of which has not been paid) and spend them not in the way of Allah, announce unto them a painful torment. On the Day when that (Al‑Kanz: money, gold and silver, the Zakah of which has not been paid) will be heated in the fire of Hell and with it will be branded their foreheads, their flanks, and their backs, (and it will be said unto them:) ‘This is the treasure which you hoarded for yourselves. Now taste of what you used to hoard’} (At-Tawbah 9:34-35)
Allah Almighty knows best.