USCIS does not have an official expedited process for the N-644 Form.
USCIS may consider requests for expedited processing on a case-by-case basis if the applicant can demonstrate that they meet one or more of the USCIS expedited criteria, such as severe financial loss, an emergency, or compelling humanitarian reasons. The request for expedited processing must be made in writing and include documentation to support the request.
It is important to note that USCIS has sole discretion to approve or deny expedited requests, and there is no guarantee that the request will be granted.