Which courts in the federal system have original jurisdiction within their regions

Answer: United Sates district court.

Explanation: United Sates district court are trial courts that operates within the United States federal court, this court hears both criminal and civil cases within their district.

In the United states, every district court has a bankruptcy court associated with it, also there is at least a courthouse in every federal judicial district, although a good number of districts can boast of more than one. Every district court in the United States has a formal name which bears the name of the district. For example, the United States District Court for the Western District of Texas.