I think you are trying too hard, Fatema,
The opening sentence of "I have come across to know that your university is offering the International Marketing course. I, “abc”, am ambitious to enroll in the aforementioned course and become an esteemed student of your prestigious institute" is difficult to read, contains groups of words that are meaningless to me ( "have come across to") and the language doesn't sound natural ("esteemed student"
The principle of "less is more" applies here I think.
I suggest you redraft it using less flowery language initially and fewer and shorter paragraphs so it's more direct. We can then tweak it for you.
Good luck