You can consider to reopen or appeal the USCIS' decision to deny your H-1B status application by filing USCIS Form I-290B - Notice to Appeal or Motion. You can download the form from USCIS website for free, but you need to pay a form filing fee, and need to check the USCIS website for the latest filing fee.

The most common reason for H-1B denial is that USCIS is not satisfied the employer submitted documents to establish the "employee- employer relationship." You can use the Form I-290B to appeal the denial, or file an Motion To Reopen (MTR) your case. But filing the Form I-290B itself does not guarantee that your case will be reopened or be approved. If your case can be reopened, the appeal process can take several months or even more than half year. During the this time, you can not work in the U.S. with the H-1B status.