What is a quasi criminal trial?

It is how you try a case against a quasi-criminal. A full criminal case would have a judge and possibly a jury. If you go before a hearing officer, or a magistrate, there probably would not be a jury, but then you could not be sentenced to jail. Courts are doing all sorts of nonsensical things to find ways of getting money from anyone who appears before them.

I have no idea since I do not practice criminal law.

No such thing.where did you get that term?

According to 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."[1] 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.[2] 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."[3] 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.[1] [4] In some cases, a court may impose asset forfeiture or another penalty.[5] 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.[6]