As a result of losing the first Sino-Japanese war, China had to cede Taiwan to Japan in 1895. The Japanese went through phases of let-the-Taiwanese-be-Taiwanese alternating with phases where they tried to assimilate the Taiwanese into Japanese culture.
During one of the assimilationist periods, Japan imposed the use of Katakana to show the Taiwainese pronunciation of Chinese script characters. Unfortunately, spoken Taiwanese is more complicated than spoken Japanese. Taiwanese is a tonal language which distinguishes between aspirated (“breathy”) and unaspirated (“not breathy”) consonants; it also has a few more vowels and consonants than Japanese.
To compensate, they decorated the syllables. They put marks to the right of the words (which were always written top-to-bottom) to show what tone the word should have and whether the vowel was nasal or not. They put horizontal bars over “s-” syllables to make “ch-” syllables; they put dots under the syllables to show aspiration.
There were also some quirks in the spelling. If a syllable only had a consonant and one vowel, the vowel was repeated, making the initial characters almost alphabetic. However, if there were lots of vowels in a syllable, the first vowel would be part of the initial syllable. Thus, “ki” would be written with “ki”+”i” characters, but “kiau” would be spelled with “ki”+”a”+”u” characters.
Pretty much after Japan got relieved of its administration of the island, the Taiwanese elected to discontinue use of Taiwanese kana.