Abstract The effect of magnetic gap and finite quasi-particle lifetime in topological insulator-based ferromagnet/f-wave superconductor (TI-based FM/f–wave SC) junctions is theoretically investigated by using the modified Blonder-Tinkham-Klapwijk (BTK) theory. Two types of pairings, f1 and f2–waves for SC, are considered. The results indicate that shortening the finite quasi-particle lifetime can lead to a transformation of energy-gap peaks into a zero-bias peak in tunneling conductance spectrum, as well as a transformation of energy-gap dips into a zero-bias dip in shot noise spectrum, ultimately resulting in the smoothing of both the zero-bias conductance peak and the zero-bias shot noise dip. An increase in magnetic gap can suppress tunneling conductance and shot noise when conventional Andreev retro-reflection dominates but enhance them when specular Andreev reflection is dominant. Both conventional Andreev retro-reflection and specular Andreev reflection can be enhanced by increasing quasi-particle lifetime. When Fermi energy equals the magnetic gap, tunneling conductance and shot noise values become zero across all energy ranges. These findings not only contribute to a better understanding of specular Andreev reflection in TI-based FM/f–wave SC junctions but also provide insights for experimentally determining the f-wave pairing symmetry.