The effects of confinement potentials of the first and second materials, core size and first shell thickness on the confinement of electron, electron-donor atom, and exciton in cylindrical core/shell/shell quantum dot (CSSQD) are studied taking into account the finite confinement potential model. The confinement of charge carriers in CSSQD with two finite confinement potentials models of the barrier materials are studied. Within the effective mass and parabolic band approximation, the 3D time-independent Schrödinger equation has been resolved. To obtain the ground state quasiparticles energies, we have used the variational technique. Our results show that the donor atom and exciton binding energy, as well as the electron energy, strongly depend on the core radius, first shell thickness, confinement potentials of the barrier materials, and their structures (A and B). Moreover, the confinement potential effect of the first material on the energies is more pronounced when their thickness is large and the core radius is small. So, the external potential effect is more significant when the first shell thickness and potential are small. Also, The binding energy of an on-center (off-center) donor atom is greater (weaker) than that of the exciton, whatever the structure of the confinement potential. In addition, the transition from a type-A to a type-B confinement system has been observed. The findings might be used to modify the electronic and excitonic properties in nanomaterials science.