Hutson is asking for $13 million more than what Mayor Cantrell proposed for her office.
Lawyers for the boy's parents say the warrants were unconstitutional and violated state law.
Judge Elizabeth Foote called the conditions at David Wade "inhumane."
Over 10,000 fewer people were in prison for nonviolent crimes in 2021 than in 2016.
The decision will impact around 1,500 cases.
The pardons could affect roughly 10,000 cases in New Orleans.
Analysis shows there have been seven summonses issued in New Orleans in 2022, down from hundreds or thousands in previous years.
Sheriff Susan Hutson has faced ongoing criticism over lack of transparency since she took office in May.
Group says the statistics show a need for alternative, non-police responses.
Mayor Cantrell has signed a $1.3 million contract with a non-profit to provide behavioral health crisis response services.