L1A Blanket Visa rejected a week ago. Do I can apply H1B this year ...?

The company's can apply for either or both if they qualify and you meet the requirements, it does not matter on merits.

You can apply for both an H-1B cap case and an individual L-1A petition with the USCIS despite the Blanket L-1 denial. Whether or not the denial will impact the USCIS filed cases depends on the reason for the denial. Your employer's immigration counsel can best address your concerns since they have your immigration file.

Hello - your company may petition on your behalf in both the L-1 and H-1B. In the former case, you will need to overcome the grounds for denial if they relate to the new L-1 petition. In the latter case (H-1B), time is of the essence, and the company will need to retain counsel and move very, very rapidly if you are to have a shot at making the FY 2016 lottery. We wish you the best from Chicago! Riddhi Jani, Esq. [email protected]