USCIS Announcement of Processing Fy2020 H-1b Cap Petitions
As per today's announcement by USCIS Premium Processing is available for FY2020 cap cases and they shall begin premium processing on or after May 19, 2019, for all cap-subject premium processing cases.
All H-1B cap-subject petitions can be filed concurrently with premium processing request except the H-1B petitions that are not seeking Change of Status in the United States (seeking consular notification/processing).
H-1B petitions that are not seeking Change of Status may apply for premium processing once premium processing begins that is likely in June 2019 onwards.
The lottery will be implemented as per new rule by reversing the order by which USCIS selects H-1B petitions under the H-1B regular cap and the advanced degree exemption. This means whether one is eligible for master's cap or not will go through regular cap first and then whoever is remained or not selected in the regular cap, will be included advanced degree cap lottery.
In Summary, USCIS implements Premium Processing in two phases as stated above rather than completely suspending for cap cases.