  This paper is devoted to present new definition of complexity factor for
static cylindrically symmetric matter configurations in
$f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity. For this purpose, we have considered
irrotational static cylindrical spacetime coupled with a locally anisotropic
relativistic fluid. After formulating gravitational field and conservation
equations, we have performed orthogonal splitting of the Riemann curvature
tensor. Unlike GR (for spherical case) the one of the structure scalars
$X_{TF}$, has been identified to be a complexity factor. This factor contains
effective forms of the energy density, and anisotropic pressure components. Few
peculiar relations among complexity factor, Tolman mass and Weyl scalar are
also analyzed with the modified $f(R,T,R_{\mu\nu}T^{\mu\nu})$ corrections.
