A polyelectrolyte (PE) chain in the vicinity of an oppositely charged surface can exhibit a discontinuous transition from the adsorbed to the desorbed state once the electrostatic attractive interactions are not strong enough to overcome the entropic losses caused by the PE-surface adsorption. In the context of PE-protein interactions, the heterogeneity of the charge distribution and the effects of a low dielectric permittivity underneath the surface are crucial. Studies of the combined effects of these two properties are very sparse, especially in the spherical geometry; we thus fill this gap here. We study the adsorption of PE chains onto spherical particles with heterogeneously charged surfaces, with the main focus on the critical-adsorption conditions and the effects of a low-dielectric core. Metropolis Monte Carlo simulations are employed, with the PE exploring the phase-space around the binding particle in the canonical ensemble. Two adsorption-desorption transitions are observed when the particle possesses a net charge of the as that of the PE, resulting in behavior of the critical charge density required for the PE-particle electrostatically driven adsorption. An increased affinity between the PEs and low-dielectric particles with variable heterogeneous charge distributions is observed, in contrast to the behavior detected for homogeneous low-dielectric particles. This higher affinity occurs when the Debye screening length in the solution becomes comparable to the dimensions of a patch of the opposite sign to the PE. A number of real-life applications of the considered PE-particle system is presented in the discussion, in particular regarding the properties of the complex formation between various PEs and globular proteins featuring a dipolar-type distribution of electric charges on their surfaces, such as insulin and bovine serum albumin.