There’s the International Phonetic Alpabet for all languages.
But is there any native/national English phonetic system/alpabet with has its own sound symbols, transcriptions etc.?

Question

There’s the International Phonetic Alpabet for all languages. 
But is there any native/national English phonetic system/alpabet with has its own sound symbols, transcriptions etc.?

Answer

Yes. There are several. There's no single official version because there's no organisation that regulates the language. But if you do a quick internet search or use a dictionary you will find example. Both Oxford and Merriam Webster dictionaries use IPA