What term describes jurisdiction that pertains solely to the state, particularly in violation of state law?

The correct term that describes jurisdiction pertaining solely to the state, especially in relation to violations of state law, is proprietary jurisdiction. This type of jurisdiction emphasizes the state's authority over certain matters, particularly those of local concern that fall within its legal framework. Such matters often include state crimes, regulatory issues, and specific local governance, allowing the state to exercise control independently of federal influence.

This concept is pivotal in understanding the division of powers between state and federal authorities, as it underscores that specific legal matters are managed exclusively by state law, not subject to federal intervention. This distinction is critical in jurisdictions where state laws are unique and tailored to local populations and issues, thereby reinforcing the state's role in law enforcement and legal proceedings.