Neutrosophic topological structure can be applied in many fields, viz. physics, chemistry, data science, etc., but it is difficult to apply the object with periodicity. So, we present this concept to overcome this problem and novelty of our work is to extend the range of membership, indeterminacy and non-membership from closed interval [0, 1] to unit circle in the neutrosophic complex plane and modify the existing definition of neutrosophic complex topology proposed by [17], because we can’t apply the existing definition to some set theoretic operations, such as union and intersection. Also, we introduce the new notion of neutrosophic complex αѱ connectedness in neutrosophic complex topological spaces and investigate some of its properties. Numerical example also provided to prove the nonexistence.