Is zakat obligatory on the remainder of the amount paid as a down payment in a house construction contract that will not be completed until after two years, and is this amount considered my property?

If the money available does not exceed the remaining household expenses, then there is no zakat (definition) on it because it is a debt. However, if he owns other non-zakatable assets such as furniture or real estate, which cover the remaining payment and exceed the nisab (definition), then he pays zakat on the surplus after deducting the value of what he needs from furniture and the like.