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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The scholars held different views regarding the ending time of the ‘Ishaa’ prayer. The correct view according to the four (main) Schools of Fiqh is that the time of the ‘Ishaa’ ends at the rise of the true dawn.
The Hanafi scholar Al-Kaasaani wrote, "According to our School, the time of the ‘Ishaa’ ends when the true dawn rises." [Badaa'i‘ As-Sanaa'i‘]
The Maaliki scholar ‘Ulaysh wrote, "The preferred time of the ‘Ishaa’ lasts until the end of the first third of the night. It is also said that the preferred time of the ‘Ishaa’ lasts until dawn and that there is no time of necessity for it." [Minah Al-Jaleel]
The Shaafi‘i scholar An-Nawawi wrote, "The preferred time of the ‘Ishaa’ ends when the first third of the night has passed, and then the time of necessity starts and lasts until the break of the second dawn. This is the default opinion in our School (the Shaafi‘i School)." [Al-Majmoo‘]
The Hanbali scholar Ibn Qudaamah wrote, "It is permissible to delay the ‘Ishaa’ until midnight, and beyond midnight is the time of necessity ... it lasts until the rise of the second dawn." [Al-Mughni]
In brief, there are two times for the the ‘Ishaa’ prayer: a preferred time which starts when the twilight has disappeared and lasts until the first third of the night or its half has passed, and a time of necessity, which is after that and until the rise of dawn.
Hence, your ‘Ishaa’ prayer performed after midnight was valid, and you are not required to repeat it.
Our advice to you – after fearing Allah, the Exalted – is to hasten to perform the prayer at its preferred time, i.e. at the beginning of its prescribed time. ‘Abdullah ibn Mas‘ood asked the Prophet "Which deed is loved most by Allah?" He replied, "Performing the prayer at its due time." [Al-Bukhaari and Muslim]
Al-Haafith Ibn Hajar wrote, "Ibn Battaal said: it is deduced from this hadeeth that it is better to perform the prayer at the beginning of its prescribed time." [Fat-h Al-Baari]
Allah knows best.