I have applied for admission to post-graduation course at a few universities.
I have applied at a few universities for admission in post-graduation course.
English Language Learners Stack Exchange is a question and answer site for speakers of other languages learning English. It only takes a minute to sign up.
Sign up to join this communityIn terms of word order, they are both correct and there isn't a particular reason you should use one and not the other. You should consider amending the bits in bold below and also add punctuation:
I have applied for admission to a post-graduate course, at a few universities.
I have applied, at a few universities, for admission to a post-graduate course.