How do I check the authenticity of iPhone adapter?

you can't

only way you can be sure is if you purchase it in an apple store or official apple reseller

fakers can use real serial numbers if they wish and they can use the same packing, well they would sort of being lazy fakers if they did not

FWIW ... For future reference, if you perform a search on this forum, you will find literally dozens of posts on this exact topic and would have found out the same answer that Rudegar has just provided you.