Praise be to Allah.
If the conditions of zakaah being due are met with regard to this money, such as it reaching the nisaab and one full (hijri) year having passed since it was acquired, then zakaah must be paid on it, even if this money is being saved to meet a specific need such as accommodation, education or maintenance.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked in Majmoo’ al-Fataawa (14/130):
I am saving money from my salary each month. Do I have to pay zakaah on this money, knowing that I am saving this money to build myself a house and to pay the dowry for my marriage soon, in sha Allah, and I have been saving this money for several years in the bank because I have nowhere else to keep this money?
Wealth that is being saved to get married, to build a home or for other purposes is subject to zakaah if it reaches the nisaab and one full year has passed, whether it is gold, silver or cash, because of the general meaning of the evidence which indicates that zakaah is obligatory on that which reaches the nisaab and one full year has passed, with no exceptions.
As for putting the money in riba-based banks, that is not permissible, because that is helping them in sin and transgression. But if that is done out of necessity, then it is permissible, but it should be without interest. End quote.
He was also asked in Majmoo’ al-Fataawa (14/126)
If a person is saving money with the aim of getting married, is it exempt from zakaah?
He replied (may Allah have mercy on him):
Zakaah is not waived if one has the intention of getting married; the same applies to one who is collecting money to pay off a debt or to buy real estate to set up as a waqf or to buy a slave in order to set him free. Rather zakaah must be paid in all cases, if one year has passed since the money was collected, because Allah, may He be glorified, has enjoined zakaah on the accumulated amount, and He has not stated that such purposes could mean that it is waived. Zakaah increases wealth and does not decrease it; it purifies it and purifies its owner, as Allah says (interpretation of the meaning):
“Take Sadaqah (alms) from their wealth in order to purify them and sanctify them with it”
And the Prophet (peace and blessings of Allah be upon him) said: “Wealth does not decrease because of charity.” Narrated by Muslim (2588). End quote.
In Fataawa al-Lajnah al-Daa’imah (9/381) it says:
Zakaah is due on money that has been saved for building if one full year has passed and it reaches the nisaab by itself or when added to other wealth that is subject to zakaah, such as cash or trade goods. End quote.
This was stated by Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) in his fatwas, and we have quoted his fatwa in the answer to question no. 41805.
The most correct of the scholarly views is that zakaah must be paid on the wealth of one who owes a debt, and the one who is paying a debt in instalments, because a debt for which payment has been deferred does not mean that zakaah is waived on the wealth that is being saved if it reaches the nisaab, because zakaah is an act of worship that is required of the one who has wealth, based on the general meaning of the verses and ahaadeeth which enjoin paying zakaah. This has been discussed in detail in the answer to question no. 22426.
Based on this, you have to pay zakaah on the money that has been saved. As for the money which you gave as a down payment to buy the house, you do not have to pay zakaah on it because it is no longer in your possession since you gave it to the seller.
And Allah knows best.