On application I write "I, Sushanta Majhi, a student of your school state that" so is it correct, should am be used as helping verb in-place of a.
It's grammatically correct.
It just would sound a little silly in most situations, as if you are writing a personal manifesto, and not an application. The use of the verb "state", since whatever you write is "stated" so it's unnecessary. Your name and status are probably already known so the simpler replacement would be to cut this whole phrase and just write the thing that you "state".