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Motivated by a problem of optimal harvesting of natural resources, we study acontrol problem for Volterra type dynamics driven by time-changed L\'evynoises, which are in general not Markovian. To exploit the nature of the noise,we make use of different kind of information flows within a maximum principleapproach. For this we work with backward stochastic differential equations(BSDE) with time-change and exploit the non-anticipating stochastic derivativeintroduced in [15]. We prove both a sufficient and necessary stochastic maximumprinciple.

Stochastic Volterra equations with time-changed L\'evy noise and maximum principles