From an email message which I received earlier today:
The U.S. Supreme Court Fellows program is now accepting applications for the 2016-2017 term. The fellowship, which is open to both junior and mid-career candidates, might be of interest to both current and aspiring academics as well as graduating and recently graduated law students.
Four fellowships are awarded each year, and each fellowship is unique in its scope and focus. Interested persons can read more about the program at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2378584.