The effect of location of the constituent carriers in different confining potentials on the binding energy and diamagnetic susceptibility of an exciton in a GaAs/Al0.3Ga0.7As Quantum Ring (QR) has been investigated by variational method. The inter-particle separation of electron and hole in both square and parabolic quantum rings along the radial and axial directions and hence the spatial extension of the excitonic wavefunction is studied. Unlike other low dimensional structures, QR hardly allow barrier penetration of the carrier because of their topology and the same is investigated by considering the particles at the edge of the ring for the two different confining potentials. Height of the ring has been tuned to understand the behavior of the excitonic states along the axial direction. The change in diamagnetic susceptibility for two different confining potentials has also been calculated for various ring widths. The square and parabolic potential shows a major difference in the interface which can be witnessed from the change in binding energy and susceptibility of the exciton for various locations of electron and hole.