What you’re describing are known as demonyms, AKA words for a people or nation. The names can come from a lot of different sources:
* -ish has Germanic roots, and is generally used to describe place names that the English have known about since the Early Middle Ages, when the English language had a far more Germanic vocabulary.
* -ese comes from Latin via French, and has a lot of cognates in Romance languages like Portuguese or Italian. The reason a lot of East Asian names use this (Chinese, Japanese, etc.) is because a lot of explorers and travelers to East Asia were Portuguese, and the names entered English via reports from Portugal.
* -an and -ian come from Latin, so they’re generally used to describe names that either come from Latin, or are at least pseudo-Latin sounding.
* -ic also comes from Latin, and is also used to describe place names with Greek or Latin roots. Why do some use -ic while some use -ian? Probably because that’s what the Romans did and we just copied that.
* -ite comes from ancient Greek via Latin. It’s uncommon nowadays, and generally only sees use today as a deliberate neologism (e.g., “Brooklynite”).
* -i comes from words adopted from Semitic languages like Hebrew and Arabic (Israeli, Omani, etc.).
And then there are a lot of exceptions, generally because we adopted the word straight from another language and didn’t change it too much (e.g., “Greek” coming from Latin *graecus*).
#Edit:
About the etymologies that people keep asking about in the replies:
* **Greek:** From Latin “Graecus.”
* **French:** From Old English “Frencisċ” (Frankish). The -isċ evolved into the modern English -ish.
* **Michigander:** Deliberate pun on the word “gander” (as in a male goose).
* **Norwegian:** From the medieval Latin name for Norway, “Norvegia.”
* **Glaswegian:** A pun by the people of Glasgow based on “Galwegian,” which itself was a pun by the people of Galway based on “Norwegian.”
* **Haligonian:** Based on a legend that the town of Halifax’s Old English name as “halig feax” (holy hair).
* **Corfiot:** Based on the word “Cypriot,” from the Greek “Κυπριώτης” (*Kupriótis*), to describe someone from Cyprus. Ironically enough, not used in Greek, because the Greek name of the island of Corfu is Kerkyra.
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