Where I got it from said it was not part of the original Hagia Sophia but it is adjacent. But when I just looked it up it said it’s in Istanbul (got that part right!) but totally separate. Also is called the Blue Mosque. Would love to visit Istanbul one day.
Yes, the Blue Mosque is about 400 metres away from Hagia Sofia (both are worth seeing, but for me, Hagia Sofia / Ayasofya is more impressive). Istanbul is a fantastic city to visit (Mosques, Cisterns, Topkapi Palace, the Walls, the Fortress of the Seven Towers, the 1453 exhibition, trips on the Bosporus, and the fabulous food: I highly recommend it.
MATTHEW'S ISLAND 
Not Hagia Sophia (aka Ayasofya), which was built almost a thousand years earlier.
Where I got it from said it was not part of the original Hagia Sophia but it is adjacent. But when I just looked it up it said it’s in Istanbul (got that part right!) but totally separate. Also is called the Blue Mosque. Would love to visit Istanbul one day.
Yes, the Blue Mosque is about 400 metres away from Hagia Sofia (both are worth seeing, but for me, Hagia Sofia / Ayasofya is more impressive). Istanbul is a fantastic city to visit (Mosques, Cisterns, Topkapi Palace, the Walls, the Fortress of the Seven Towers, the 1453 exhibition, trips on the Bosporus, and the fabulous food: I highly recommend it.