Despite significant advances in understanding and modeling size segregation of non-cohesive granular materials, segregation of cohesive materials remains much less understood. Here we consider segregation of cohesive mixtures of size-bidisperse particles over a wide range of flow conditions and levels of cohesion for particle-size ratios less than six in gravity-driven bounded heap flow using DEM simulations. When particle species have identical surface energy densities, low levels of cohesion leave segregation largely unchanged from the cohesionless case, while higher levels of cohesion reduce segregation significantly. Various contact models for cohesion, each with different force discontinuities and hysteresis effects, give consistent segregation results with only minor differences. When species have different surface energy densities, the relative strengths of large-large, large-small, and small-small particle contacts change, which can, in turn, alter the overall segregation. Strong large-large particle cohesion enhances cohesive clustering of large particles and therefore increases segregation due to the increase in the effective size ratio of clustered large particles to individual small particles. Strong small-small particle cohesion enhances cohesive clustering of small particles and reduces segregation due to a decrease in the effective size ratio of individual large particles to clustered small particles. This selective clustering mechanism is supported by measurements of contact persistence and the associated changes in the segregation velocity. This material is based upon work supported by the National Science Foundation under Grant No. CBET-2429545 and by the International Fine Particle Research Institute.