Angular distributions of projectile-like fragments (PLFs) have been measured in the reaction ¹⁹F + ⁶⁶Zn at E_lab = 61, 82, 92, and 109 MeV to understand their formation in the low energy domain (< 7 MeV nucleon). In this energy range,  maximum angular momentum ‘l_max’ in the reaction is lower than or close to the critical or limiting angular momentum for complete fusion ‘l_lim(CF).’ The sum-rule model was modified to explain the cross sections of PLFs in the present study. For the first time, the modified sum-rule model, with a competition of incomplete fusion (ICF) reaction with complete fusion below l_lim(CF) reasonably reproduced the cross sections of PLFs in the beam energy range of the present study. It was observed that the cross sections of lighter PLFs fall more rapidly with decreasing beam energy compared to those of heavier PLFs, suggesting a change in the reaction mechanism from heavier to lighter PLFs. Transfer probabilities for peripheral collisions were calculated within the framework of a semiclassical formalism. The parameters of the nuclear potential required for the calculation of transfer probability were obtained by fitting the elastic scattering data measured in the present work. Calculated transfer probabilities were significantly lower compared to the corresponding experimental values, suggesting a significant overlap of the projectile and the target nuclei in incomplete fusion reactions. The present analysis showed that the overlap of the projectile and the target nuclei increases with increasing mass transfer at a given beam energy and for a given PLF, overlap increases with increasing beam energy.