The Ninth Circuit has determined that federal courts lack jurisdiction to stay a non-citizen’s removal during the pendency of the adjudication of his motion to reopen by the Board of Immigration Appeals. Such federal court intervention is precluded by 8 USC 1252(g), and is not restored by the Suspension Clause.
The full text of Rauda v. Jennings can be found here:
https://cdn.ca9.uscourts.gov/datastore/opinions/2021/08/13/21-16062.pdf