Ukrainian
In Ukrainian, yat has been traditionally represented /i/ or /ji/. In modern Ukrainian orthography its reflexes are represented by <і> or <ї>. However, in some phonetic orthographies from the nineteenth century, it was used to represent /ʲe/ or /je/. This corresponds more with the Russian pronunciation of yat rather than actual word etymologies. The modern Ukrainian letter <є> has the same phonetic function. Several Ukrainian orthographies with the different ways of using yat and without yat co-existed in the same time during the 19th century, and most of them were discarded before the 20th century. After the middle of 19th century Orthographies without yat dominated in the Eastern part of Ukraine and after the end of 19th century they dominated in Galicia. However, in 1876–1905 the only officially legalized orthography in the Eastern Ukraine was based on Russian phonetic system (with yat for /je/) and in the Western Ukraine (mostly in Carpathian Ruthenia) orthography with yat for /i/ was used before 1945.
'New yat' is a reflex of /e/ (which merged with yat in Ukrainian) in closed syllables. New yat is not related to the Proto-Slavic yat, but it has frequently been represented by the same sign. Using yat instead of <е> in this position was a common after the 12th century. With the later phonological evolution of Ukrainian, both yat and new yat evolved into /i/ or /ji/. Some other sounds also evolved to the sound /i/ so that some Ukrainian texts from between the seventeenth and nineteenth centuries used the same letter (⟨и⟩ or yat) uniformly rather than variation between yat, new yat, <и>, and reflex of <о> in closed syllables, but using yat to unify all i-sounded vowels was less common, and so 'new yat' usually means letter yat in the place of i-sounded <е> only. In some etymology-based orthography systems of the nineteenth century, yat was represented by ѣ and new yat was replaced with ⟨ê⟩ (⟨e⟩ with circumflex). At this same time, the Ukrainian writing system replaced yat and new yat by ⟨і⟩ or ⟨ї⟩.
Read more about this topic: Yat