When is premium processing starting

USCIS announces that they will start premium processing again starting from June 08, 2020. H1b , I-140 is the main category USCIS initially thinking to resume premium processing.

Effective June 1, 2020, USCIS will accept Form I-907, Request for Premium Processing Service for all eligible Form I-140 petitions.

Effective June 8, USCIS will accept premium processing requests for: 

• H-1B petitions filed before June 8 that are pending adjudication and are cap-exempt (for example, petitions filed by petitioners that are cap-exempt and petitions filed for beneficiaries previously counted toward the numerical allocations). 
• All other Form I-129 petitions (non H-1B petitions) for nonimmigrant classifications eligible for premium processing filed before June 8 that are pending adjudication.

Effective June 15, USCIS plans on resuming premium processing for: 

• H-1B petitions requesting premium processing by filing an I-907 concurrently with their I-129 (or request for a petition filed on or after June 8) and are exempt from the cap because: 
• The employer is cap-exempt or because the beneficiary will be employed at a qualifying cap-exempt institution, entity or organization (such as an institution of higher education, a nonprofit research organization or a governmental research organization); or 
• The beneficiary is cap-exempt based on a Conrad/IGA waiver under INA section 214(l).

Effective June 22, USCIS plans on resuming premium processing for all other Form I-129 petitions, including: 

• All H-1B cap-subject petitions (including those for fiscal year 2021), including change of status from F-1 nonimmigrant status, for both premium processing upgrades and concurrently filed I-907s. 
• All other Form I-129 petitions for nonimmigrant classifications eligible for premium 

Reference:

https://www.uscis.gov/news/alerts/uscis-resumes-premium-processing-certain-petitions