Do the employers take back or charge the visa fees from an employee ?

Hi,

Do companies or employers usually ask an employee to pay the employer the entire fees of the H1B if the employee either leaves the organization or gets his visa transferred or something ? I’d like to know if the top IT cos of India do this ?

It depends on your company policy. It is not legal though. The big IT companies will never ask for H1 processing fee even if you leave them but they might have a clause with you that you would pay for liquidated damages. Furthermore they can not make you sign anything which says that you will have to pay a certain amount if you leave. That is illegal as well.