According to the website
The records in this series are the direct result of "An act for the Gradual Abolition of Slavery" passed by the New Jersey Legislature on 15 February 1804 (P.L. 1804, chap. CIV, p. 251). This law pronounced every child born to a slave mother after 4 July 1804 "free" at birth, but bound as a servant to the owner of the mother until the age of twenty-five for males and twenty-one for females. Any person entitled by the law to such bound service was required to file with the county clerk, within nine months of the birth of the child, a written certificate containing the name of the slave owner and the name, age and sex of the child. The clerk in turn was directed to record the information in a special book for this purpose. The penalty for neglecting to deliver such a certificate was $5 plus an additional $1 for each month of delinquency. The law also allowed for the abandonment of such children by the owners of their mothers at the age of one year. In this case, the child would become a ward of the local overseers of the poor; the slave owner was required to file a notification of abandonment with the county clerk.