Summary: In the present paper, we propose to investigate a new subclass \(\Sigma_M^{\ast,p,q}(h,\mu,\lambda,k,\gamma)\) of meromorphic functions associated with linear operator defined by means of convolution in the exterior of the unit disk \(\nabla:= \{z\in\mathbb{C} : 1 < |z| <\infty\}\). We study the behaviour of initial coefficients \(b_0\), \(b_1\) and \(b_2\) for the function in this newly constructed class. Some interesting remarks of the results presented here are discussed. Our results generalize and improve some of the previously known results of other researchers.