Where does “Кадамжай” come from?

Кадамжай (Kyrgyz) comes from Kyrgyz жай, from Proto-Turkic yāy — summer, spring.

Ancestry of “Кадамжай”, step by step

Кадамжай traces back through two separate lines of ancestry.

via Kyrgyz жай

StepLanguageWordMeaning
1Kyrgyzжайsummer
2Proto-Turkicyāysummer, spring

via Kyrgyz кадам

StepLanguageWordMeaning
1Kyrgyzкадам—
Every word from Proto-Turkic yāy →Every word from Kyrgyz жай →