This paper presented a new Ruscheweyh fractional derivative of fractional order in the complex conformable calculus sense. We applied the constructed complex conformable Ruscheweyh derivative (CCRD) on a certain base of polynomials (BPs) in different regions of convergence in Fréchet spaces (F-spaces). Accordingly, we investigated the relation between the approximation properties of the resulting base and the original one. Moreover, we deduced the mode of increase (the order and type) and the Tρ-property of the polynomial bases defined by the CCRD. Some bases of special polynomials, such as Bessel, Chebyshev, Bernoulli, and Euler polynomials, have been discussed to ensure the validity of the obtained results.