What power does the executive branch have over the judicial branch?
The President (Executive Branch) has the power to appoint US Supreme Court justices and other (Article III ) federal judges. subject to approval by the Senate. He can and does choose judges who subscribe to his own legal philosophy and so can possibly shape future court opinions. The judges serve for life and their stance on future cases is hard to predict in many cases.
The president can also grant pardons for federal offenses.