All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
After intensive research, we have not come across a book by Ibn Hajar Al-‘Asqalaani or by Ibn Hajar Al-Haytami called Takhreej Al-Mishkaat.
However, there is a book by that name written by the prominent scholar Shaykh Al-Albaani and he used to refer to it in some of his writings, such as As-Silsilah As-Saheehah.
Allah knows best.