Ge’ez, aslo called Ethiopic, is the only Old World abugida outside of Southest Asia and the only abugida that is not clearly derived from Brahmi. (Aside from Kharosthi, of course, which maybe spawned Brahmi.)
However, it took a long time for the vowel decorations to appear. For the first 500 years of Ge’ez’ life, it was a rather ordinary offshoot of South Arabian (except for the fact that it is the only offshoot of South Arabian). In around 200-300 AD, however, they started decorating the consonants with vowel information, with credit generally being given to Saint Frumentius for that invention. (He also is credited with the first translation of the Bible into Ge’ez, the spoken language of the area, and spreading Christianity widely in what is now Ethiopia.)
Frumentius’ life story doesn’t show him spending time in India, but Ethiopia was an ocean country, and Frumentius might have come into contact with Indic abugidas via Indian traders. (Frumentius was the boyhood tutor for the king Ezana, and coins with Ezana’s name were found in India.)
Ge’ez started out being written right-to-left, like most of the other Semitic abjads, but switched to left-to-right, perhaps because of the influence of Greek.
Ge’ez is still used in Ethiopia to write the national language, Amharic. With a population of 85M in Ethiopia (for comparison, Germany has 80M people), Ge’ez is a significant writing system.
Ge’ez uses something that looks like a semi-colon to indicate word breaks.