I stand corrected. Common law writs. Admonish me.
The problem is that there is no federal common law. The All Writs Act, 28 USC ยง 1651, authorizes then Supreme Court and other federal courts to “issue all writs necessary or appropriate in aid of their respective jurisdictions and agreeable to the usages and principles of law,” but that does not confer any additional jurisdiction on the Supreme Court.
SCOTUS’s jurisdiction here is limited to: (1) appellate jurisdiction to hear a petition for certiorari from a final judgment of NY’s highest court, the NY Court of Appeals; or (2) jurisdiction to hear an original petition for habeas corpus if (and only if) Trump is in “state custody.” There is no jurisdiction yet because (1) the case hasn’t even been heard by, let alone ruled on by, the NY Court of Appeals; and (2) Trump is not currently in state custody.
As I’ve said elsewhere, Judge Merchan can effectively preclude any SCOTUS review of this case before the election by simply allowing Trump to remain free pending his appeal. Of course, since he’s proven he’s a political actor, whether he does so probably depends on what he thinks will politically benefit Biden and the Democrats most: Denying Trump the chance at vindication through reversal of the conviction, or the spectacle of SCOTUS potentially stepping in to keep Trump out of jail (which they’ll use to further attack SCOTUS’s legitimacy).