The Confederate Constitution provided for a Supreme Court. In fact it's almost identical to the US Constitution in those passages.

Once the permanent congress was elected and seated a judicial committee was formed recommendations were made, and bills were passed all regulating and defining the court. The primary bill to actually establish the court never passed. The Senate sent a final bill to the House on March 19th, 1863. A number of bill amendments were proposed, it went back and forth and in and out of committees at a very slow pace. Finally the Senate tabled the bill in March 14th 1865.

So while in theory the CSA had a Supreme Court, in practice it was never organized, it never had justices, and never heard any cases.

The Confederate Constitution defined the Supreme Court of the CSA to be the majority of all the "District Judges" as long as their was a quorum. As a practical matter, the relatively short duration of the CSA and is organizational character meant that there was never an actual Confederate Supreme Court and the various supreme courts of the states in the CSA were the highest judiciary body during its duration. See George, 6 Virginia Law Register N. S. The Supreme Court of the Confederate States of America, 1920.

No neither they able to develop their Supreme Court 100% nor hear any cases.