Abstract Magnetic Weyl semimetals (mWSMs) enable spin-resolved optical responses at zero magnetic field via their intrinsic topological magneto-optical effects, making them an ideal material platform for spin-selective absorption. However, most existing mWSM-based absorption structures rely on periodic photonic crystal, whose single resonance channel is insufficient to support multichannel parallel spin information processing. Here we construct a heterostructure composed of a Fibonacci quasi-periodic photonic crystal and an mWSM thin film, and systematically investigate its spin-dependent absorption characteristics by using the 4×4 transfer matrix method. Results show that the self-similar fractal energy bands of the quasi-periodic structure satisfy the optical Tamm states phase matching condition in three reflection bandgaps simultaneously, inducing triple-band near-perfect absorption with prominent spin splitting in each band. Furthermore, Weyl node separation, Fermi level and dielectric layer thickness act as independent tuning parameters to adjust the resonance frequency and absorption intensity of the three absorption bands respectively. This study breaks the channel number limitation of periodic configurations and provides a feasible approach for designing integrated multichannel spin photonic devices.