بَاعَ has a long middle vowel, but that vowel cannot remain before certain consonantal endings. The alif drops, while kasrah on the first root consonant reflects the original yāʾ.
Word / formMeaning / explanation
بَاعَhe sold.
بِعْتُI sold.
بِعْنَthey (women) sold.
The invented “بَاعْتُ” is not correct; the proper form is بِعْتُ. The root is unchanged: this is a predictable phonological contraction.