No, Troy was not part of the Persian Empire.
Troy, an ancient city located in what is now northwest Turkey, is best known for its role in Greek mythology and the Trojan War. The city flourished during the late Bronze Age, well before the rise of the Persian Empire, which emerged in the mid-6th century BCE under Cyrus the Great.
Throughout its history, Troy was variously influenced by different cultures, including the Hittites and later the Greeks. By the time the Persian Empire began to expand, Troy was already in ruins and had lost its significance as a major urban center. Thus, it never fell under Persian control.
In summary, Troy predates the Persian Empire and, due to its decline, was not incorporated into that vast empire that controlled many regions of the ancient world.