In recent years, traditional zero-correlation zone (ZCZ) sequences are being studied due to support interference-free quasi-synchronous code division multiple access (QS-CDMA) systems. However, in cognitive radio (CR) network, it is desirable to design ZCZ sequences having spectral null constraint (SNC) property to achieve low spectral density profile. This paper focuses on the construction of SNC-ZCZ sequences having flexible support, where support refers to a collection of indices corresponding to non-zero entries in the sequence. The proposed SNC-ZCZ sequences reduce to traditional ZCZ sequences when the size of the support becomes equal to the length of the sequence. To obtain ZCZ sequences, we first propose construction of traditional/SNC-Complete complementary codes (SNC-CCCs) using a class of extended Boolean functions (EBFs). With the help of this class we propose another class of EBFs that generates asymptotically optimal traditional/SNC-ZCZ sequences of prime-power lengths with respect to Tang-Fan-Matsufuzi bound. Furthermore, a relation between the second-order cosets of first-order generalized Reed-Muller code and the proposed traditional ZCZ sequences is also established.