We investigate the spontaneous emission (SE) of a quantum emitter (QE) near a topological insulator BiS₂X₃(X=Se,Te) nanosphere. We calculate the Purcell factor of the QE near a nanosphere of radius between 40 nm and 100 nm by first-principle electromagnetic methods using experimental parameters for describing the optical properties of the topological insulator material, with and without taking into account the topologically protected delocalized surface states. We find exceptional Purcell factors of the QE up to 10¹⁰ at distances between the QE and the nanosphere as large as half its radius in the terahertz regime. We study the SE dynamics of a QE for various transition frequencies in the terahertz and free-space decay rates, which affects inversely proportional the coupling strength between the QE and the nanosphere, in the ns to ms range. For short free-space decay times, the dynamics has strong non-Markovian features, which correlate directly with large values of well-established non-Markovianity measures and possible significant quantum speedup of the dynamics. The dynamical features become gradually Markovian as the free-space decay times become long, while the corresponding non-Markovianity measures tend to zero and the quantum speedup diminishes. For the shortest free-space decay times, we find that population remains trapped in the QE, which manifests the formation of a hybrid bound state between the QE and the electromagnetic continuum of modes as modified by the nanosphere. This work demonstrates that a BiS₂X₃ (X=Se,Te) nanosphere can provide the conditions for strong light-matter interaction on the nanoscale.