Filing an H-1B petition requesting premium processing will NOT increase the chances of obtaining an H-1B under the quota. If you request premium processing and the case is accepted for processing, the 15 day premium processing window will start no later than April 27, 2015, according to the USCIS news alert issued 4/14/2015. Please note that one seeming benefit of filing a cap subject H-1B petition with a request for premium processing is that a receipt notice may be issued faster than if filed under regular processing. Therefore, the petitioner and beneficiary may confirm sooner that the petition has been chosen in the lottery.
Source of Information:
USCIS.gov (4/14/15) News Alert:
H-1B Cap Premium Processing to Begin April 27
USCIS.gov (4/13/15) News Alert:
USCIS Completes the H-1B Cap Random Selection Process for FY 2016
USCIS.gov, 3/17/15, Web Page:
How Do I Use the Premium Processing Service?