Hi, Is it possible to apply for H1B after completing Masters In Accounting in US with 20000 Visa cap catagory?

I have H4 and accepted by a US university In masters in accounting? Will I be able to apply for H1b after the completion of my masters degree with 20000 extra quota for US students. Your reply to the matter will be highly appreciated.

Yes - you future employer should be able to, not you.