Learn Turkish: Sultanın sarayı neredeymiş? - Where was the sultan's palace apparently?

It breaks down into three parts: nerede (where / at where) plus -y- (a buffer letter used because nerede ends in a vowel) plus -miş (the reported past suffix, meaning 'apparently was').

Why use neredeymiş here instead of neredeydi (where was it)?

The regular past tense neredeydi asks a simple, direct question about a past location. By using -miş, the speaker shows they are asking about hearsay, a historical legend, or something they were told but forgot. It often translates to 'Where was it, apparently?' or 'Where did they say it was?'

Why does saray (palace) have an -ı at the end?

It forms a possessive pair with Sultanın (the Sultan's). In Turkish, when you link two nouns to show ownership, both words get a suffix. Sultan gets the owner suffix -ın, and saray gets the owned object suffix -ı, making Sultanın sarayı.