Jon  Bon Jovi's 19-year-old daughter Stephanie Rose  Bongiovi was arrested at her college in Upstate New York early this  morning after allegedly overdosing on heroin ... TMZ has learned.

According to the Town of Kirkland Police Department, cops responded to a  dorm room at Hamilton College after someone reported that Stephanie had  allegedly overdosed on heroin and was unresponsive.

Along with police,  emergency medical personnel also responded to the scene and found Stephanie  alive.

Cops say a drug task force searched the scene and found a "small  quantity" of heroin ... along with marijuana and drug  paraphernalia.

Stephanie was arrested for possession of a controlled  substance, possession of marijuana and criminally using drug paraphernalia --  all misdemeanors.

Stephanie was eventually released from custody -- and  ordered to appear in court at a later date.

Another student was also  arrested -- a 21-year-old male -- who was also charged with drug possession.

Stephanie is Jon's only daughter -- and the oldest of his 4 children  with wife Dorothea Hurley.