Is Zakat obligatory on the installment paid by the questioner to a contractor who fled with the money and did not register the apartment? And what is the prescribed and authentic supplication for recovering the money?

The advance payment made to the contractor is subject to zakat (definition) rulings based on the reason for its payment. If it was for work completed on the building, then there is no zakat on it because its ownership has transferred to the contractor. However, if the contractor took it and absconded with it without providing anything in return, then it falls under the ruling of usurped and stolen money. As for supplicating against the contractor, one may supplicate against him as one would against oppressors, without transgressing. The Shariah has not obligated the wronged person to recite a specific supplication.