This study presents a highly accurate, computationally efficient, and novel isogeometric beam element, named as IG - RZT((m)), whose formulation is derived by using the kinematic assumptions and "a priori" transverse-shear stress continuity conditions of mixed form of the refined zigzag theory, known as RZT((m)). Both the displacement field and geometry of the beam is approximated by using non-rational B-spline (NURBS) basis functions and the IG - RZT((m)) element accommodates only four degrees-of-freedom at each control point. Since the present formulation incorporates isogeometric analysis into the RZT((m)) theory, it provides various advantages for displacement and stress analysis of thin/thick composite beams such as high-order continuity representation and simple mesh refinement. Furthermore, the utilization of RZT((m)) theory within the current beam formulation enables the calculation of nonlinear transverse-shear stress variations through the thickness of highly anisotropic beams without any post-processing. Various numerical analysis are performed to validate the accuracy of the IG - RZT((m)) element and its wide range of applicability including beams with a resin-rich damage zone. Comparisons with analytic solutions and high-fidelity finite element models demonstrate the superior accuracy and practical applicability of the present formulation, especially making the IG - RZT((m)) element as an attractive candidate for modelling delamination initiation and propagation in composite structures.