All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Allah the Almighty Classifies eight categories eligible to receive Zakah as stated in the following verse: "The alms are only for the poor and the needy, and those who collect them, and those whose hearts are to be reconciled, and to free the captives and the debtors, and for the cause of Allah, and (for) the wayfarer; a duty imposed by Allah. Allah is Knower, Wise." [At-Tawbah/60].
Further, Abu Dawood narrated that Ziyad ibn al-Harith as-Suda'I said:
I came to the Messenger of Allah (PBUH) and swore allegiance to him, and after telling a long story he said: "Then a man came to him and said: Give me some of the sadaqah (alms). The Messenger of Allah (PBUH) said: Allah is not pleased with a Prophet's or anyone else's decision about sadaqattill He has given a decision about them Himself. He has divided those entitled to them into eight categories, so if you come within those categories, I shall give you what you desire.
In conclusion, building mosques isn’t one of the eight categories mentioned in the above verse. Therefore, using Zakah funds to build a mosque or help complete its construction is impermissible. However, this objective can be achieved through collecting donations and charities in accordance with the regulations of the Ministry of Awqaf and Islamic Affairs. And Allah the Almighty Knows Best.