I learned of this from the Netflix series, the Rise of the Ottomans. Below is the clip.
https://www.youtube.com/watch?v=p-NM8RMra6Q
I cannot seem to find any naturalistic explanation to this. Further, both sides reported seeing this strange light emanating from the Hagia Sophia. This tells me it isn't mere legend. Didn't know if anyone potentially knew anything about this and had some explanation of what it could have been.
What we have is a story conveyed by a single historian that would like to sell a book and no listed or spoken sources for this account. At least that’s all I can gather from this clip and the text associated with it. It is most likely an embellishment of the historical account to add grandeur and divine validity to a conquerors brutal assault. If not that then two other possibilities are mass hysterical hallucinations brought on by the stress of the situation and the power of suggestion, where only a few people may have seen something strange but then stirred the stressed crowds into a frenzy. Also, it could very well have just been lightning.
An interesting paper on the light effects inherent in the conscious construction of the dome for purposes of using light reflections to create unusual projections:
http://papers.cumincad.org/data/works/att/ijac20075207.content.pdf
We're getting lots of questions about this lately! I answered a similar question the other day, so see that comment for sources and a possible explanation.