Jeremiah was a student at Troy Middle School, and Shanise attended School 14. The superintendent of the Troy City School District, John Carmello, wrote in a letter to parents that grief counseling would be available to students after the holiday break.

“Our hearts are broken, and our thoughts and deepest condolences are with their family and loved ones during this terribly troubling time,” Mr. Carmello wrote. “The Troy City School District is a close and supportive community, and the loss of two of our innocent and promising children is especially devastating.”

Shanta Myers liked to cook, relatives told The Daily Gazette, a newspaper based in Schenectady. Jeremiah played basketball and was a member of the Troy Boys & Girls Club for six years. The club started a GoFundMe campaign for funeral expenses, and said any excess money raised would go to mental health care for people affected by the killings.

The family was found dead on Tuesday afternoon in their basement apartment at 158 Second Avenue, in a neighborhood of subdivided Victorian houses along the Hudson River. Chief Tedesco said the number of victims, their age and the way they were killed — which he declined to describe — made the crime the worst he had seen in more than 40 years in law enforcement.