What is the meaning of ㄝ?
注音符號 are symbols invented to help kids understand how to pronounce a Chinese word in Taiwan.

Before 注音符號 was invented and PingYin were imported, students learn the pronunciation by repeat the teacher's pronounce. 注音符號 has been used for almost 100 year.

In Taiwan, the words in Chinese textbooks for elementary school student are remarked by 注音符號. So students can understand how a new word pronounce without parent or teacher. Each symbol represents a pronunciation, with combinations of these symbols(maybe 1 to 3) students can easily pronounce any Chinese word.

Like this 

In most cases, 注音符號 are not be used in formal article. But several years ago, there are a new usage of 注音符號 invented by youth. This sub-culture are called 注音文(which means article mixed with 注音符號.)

With 注音文, people use a single symbol to represents a real word which pronounce alike or similarly.

The most general example is 


我ㄉ背包 => 我的背包 => my bag
拜託你ㄌ => 拜託你了 => I beg you.


Back to @Graviton's question, ㄝ read(not pronounce, each symbol have its own read and pronunciation, just like alphabets) similar( or you can say just in the same way) to 耶. 耶 is an interjection pronounce Yé, which is used to represent a happy emotion.

Example


今晚老闆請大家吃晚餐ㄝ => 今晚老闆請大家吃晚餐耶 => Boss buy everyone a dinner tonight.


Using 注音文 is not very popular now in Taiwan. Since it's not really professional, and makes you looks like a kid in a social network.

Hope these can help you. :)