It also questioned Jammu and Kashmir Deputy Superintendent of Police (DySP) Faheem Ali, who handles separatist leader Mirwaiz Umer Farooq's security, in connection with the case.
Ali is the first police officer from the state to be interrogated by the NIA.
While Geelani's elder son Nayeem is a surgeon, the younger one, Naseem, is a state government employee.
Nayeem is widely being seen as the one who would succeed his father as the leader of the Tehrek-e-Hurriyat, a separatist conglomerate comprising pro-Pakistan hardline groups.
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The NIA registered the case on May 30, accusing separatist and secessionist leaders of working in collusion with terrorist groups.
The case related to raising, receiving and collecting funds through illegal means, including through hawala channels, for funding separatist and terror activities in Jammu and Kashmir.
It also included charges of causing disruption in the Valley by pelting security forces with stones, burning schools, damaging public property and "waging war" against India.
Electronic devices and valuables worth crores of rupees were impounded.
It was the first time since the rise of militancy in the early 1990s that a central probe agency conducted raids in connection with the funding of terrorist and separatist groups.