The National Investigation Agency (NIA) will reportedly file another status report on the same.
The 24-year-old has been in the headlines after she became a Muslim, following her marriage to Jahan.
Hadiya said she had married Jahan out of her own will and not forcibly.
During the course of the hearing, Hadiya, who was born as Akhila Ashokan, also said she wanted freedom and to see her husband after the top court asked whether she would prefer to continue studies.
The top court has now directed Hadiya, who currently is in the custody of her parents, to be taken to college for her studies and that college should allow hostel facility to her.
The top court also ordered Hadiya's college dean to be her guardian after she requested for it.
Meanwhile, counsel for Hadiya's father, Rajendran, argued that the material submitted by National Investigation Agency (NIA) should be looked into, while saying a modus operandi exists for conversion.
Earlier, the NIA had submitted a status report in a sealed cover to the top court in connection with the case.