  We present a detailed spectral and temporal analysis of the black-hole
candidate MAXI~J1535$-$571 using NICER observations in September and October
2017. We focus specifically on observations in the hard-intermediate state when
the source shows type-C quasi-periodic oscillations (QPOs). We fitted the
time-averaged spectrum of the source and the rms and phase-lag spectra of the
QPO with a one-component time-dependent Comptonization model. We found that the
corona contracts from $\sim 10^4$ to $\sim 3 \times 10^3$ km as the QPO
frequency increases from $\sim 1.8$ Hz to $\sim 9.0$ Hz. The fits suggest that
the system would consists of two coronas, a small one that dominates the
time-averaged spectrum and a larger one, possibly the jet, that dominates the
rms and lag spectra of the QPO. We found a significant break in the relation of
the spectral parameters of the source and the properties of the QPO, including
its lag spectra, with QPO frequency. The change in the relations happens when
the QPO frequency crosses a critical frequency $\nu_c \approx 3.0$ Hz.
Interestingly, the QPO reaches this critical frequency simultaneously as the
radio emission from the jet in this source is quenched.
