Wikipedia
Quasi-criminal means a lawsuit or equity proceeding that has some, but not all, of the qualities of a criminal prosecution. It may appear in either a Common law or a Civil law jurisdiction. It refers to "a court's right to punish for actions or omissions as if they were criminal."
The origins of the phrase comes from the Latin language word, quasi, meaning somewhat, sort-of, alike or akin, to criminal law, as in Quasi-contract. Quasi is used "to indicate that one subject resembles another, with which it is compared, in certain characteristics, but there are intrinsic and material differences between them."
During a civil or equity trial, a court may act as if it were a criminal case to punish a person for contempt of court. In some cases, a court may impose asset forfeiture or another penalty. For example, a court has the right to punish actions or omissions of a party in a child support case as if they were a criminal, penalizing the parent with a sentence of jail time.