It depends which supreme court you are referring to. Countries have different legislation and hierarchy for courts of law.
supreme court
Starts with primary court, followed up by District court which exercises horizontal power with Resident Magistrate's Court it has greater powers though,above all is the High Court of Tanzania,and the Highes Court in the hierarchy is Court of Appeal.
Municipal Court - County Court - Circuit (or District) Court - Court of Appeals- Supreme Court.
A Magistrate's Court is lower on the scale of judicial hierarchy than a Court of General Sessions.
Supreme Court=>County Court=>Magistrate's Court (and it's divisions being: drug, koori &etc.)
Supreme Courts generally, by definition are the highest court within their hierarchy (hence the name supreme)
The hierarchy of federal courts is District Court, Court of Appeals, US Supreme Court. So, the Court of Appeals is the answer. At least if your quest is only specifying the federal judiciary.
Yes, the Court of Appeal has the authority to overturn its previous decisions, but typically it requires a strong reason or new evidence for doing so. This process is known as precedent overruling.
Basically how precedents relate to the hierarchy of courts is that all the lower level courts within the judicial system applies the rule of law or precedent that was created at the court above them. For example, since the privy council is the highest level in the hierarchy of courts, in fact, the court of appeal, the supreme, resident magistrate and even petty sessions courts would apply the decisions made in similar cases.
The High Court is the highest court because that is how the court hierarchy has placed it. Generally the most important and powerful institution is placed at the top of such an arrangement. The name of the court is irrelevant however, in the USA the highest court is the Supreme Court which is only a court of state jurisdiction in Australia. The High Court is the court that deals with appeals of all sorts, and constitutional matters.
The US District Courts (of which there 94) are the lowest level of the Federal courts.