Topological insulator nanoribbons (TI NRs) provide a useful platform to explore the phase-coherent quantum electronic transport of topological surface states, which is crucial for the development of topological quantum devices. When applied with an axial magnetic field, the TI NR exhibits magnetoconductance (MC) oscillations with a flux period of h/e, i.e., Aharonov-Bohm (AB) oscillations, and h/2e, i.e., Altshuler-Aronov-Spivak (AAS) oscillations. Herein, we present an extensive study of the AB and AAS oscillations in Sb doped Bi$_2$Se$_3$ TI NR as a function of the gate voltage, revealing phase-alternating topological AB oscillations. Moreover, the ensemble-averaged fast Fourier transform analysis on the Vg dependent MC curves indicates the suppression of the quantum interference oscillation amplitudes near the Dirac point, which is attributed to the suppression of the phase coherence length within the low carrier density region. The weak antilocalization analysis on the perpendicular MC curves confirms the idea of the suppressed coherence length near the Dirac point in the TI NR.