*

MnBi₂Te₄ is the first experimentally demonstrated intrinsic antiferromagnetic topological insulator. Its layered structure enables us to tune the physical properties by inserting an additional Bi₂Te₃ layer between adjacent MnBi₂Te₄ layers to create the heterostructure MnBi₄Te₇. High resolution Raman spectroscopy allows us to observe the inter- and intra-layer phonon modes of MnBi₂Te₄ and MnBi₄Te₇. In this study, we discuss the detailed phonon modes of few-layer MnBi_2nTe_3n+1 (n = 1,2) at cryogenic temperatures and different polarization configurations, through Raman spectroscopy with a resolution less than 0.5 cm^-1. The few-layer MnBi_2nTe_3n+1 topological heterostructures are prepared through exfoliation, and cross-verified through scanning probe microscopy.  Via cross- and co-polarized pump excitation, the family of dynamical modes including the E_g³, A_1g¹, A_1g², and A_1g³ resonances among others are identified with high-resolution. Together with first-principles density functional theory computations, peak positions and linewidths are observed, as well as interlayer Davydov splitting of the A_1g³ peak of the few-layer MnBi₄Te₇. Comparing the few-layer and bulk samples, the Raman intensities of the thin sample are significantly higher (up to ~6x) than that of the bulk samples enabling us to see the changes in phonon modes with polarization and temperature dependencies such as the Davydov splitting. Additionally, temperature dependent measurements from 4K to 294K of the few-layer sample demonstrate a trend of increasing intensities and left-shift of the Raman peaks.