Korean syllable 됬

No. In 됬다, the standard spelling is 됐다, a contraction of 되었다 (“became” or “was,” depending on the sentence).

Both are valid Hangul syllable blocks: 됬 has ㅚ, while 됐 has ㅙ. That one-vowel difference makes the typo easy to miss when typing; careful Korean uses 됐다.

What history belongs to 됬 itself?

Its history is part of Hangul’s, not a separate symbol story.

Hangul was created in 1443 and introduced in Hunminjeongeum in 1446, a text explaining the writing system for Korean. It gave Korean speakers a way to write their language without relying only on Chinese characters.

Hangul later served Buddhist, Confucian, royal, domestic, and official writing. Hunminjeongeum is also discussed in connection with the Phags-pa script, another writing system; this is a link at the script level, not a special history for this one syllable.