Seeing spurious peaks in acquired vibration data; peak frequency changes with sampling rate
Can you please advise what could be possible reason for such spurious FFT peaks?

Most likely it's your measurement setup. Good  measurements are hard to make and require careful setup, characterization, and execution.

Determine the noise floor (spectral shape and level) of your data acquisition system, just short the input and grab few spectra. If that looks good
Determine the noise floor (spectral shape and level) of you sensor: attach the sensor to something heavy that's not moving and grab few spectra. If that looks good
Build a &quot;calibration&quot; setup. Attach your sensor to a well characterized, calibrated or programmable vibration source (a shaker, or maybe a electro mechanical driver) and measure different frequencies at different levels and compare extend the expected results. Determine the frequency and dynamic limits of your setup.

In each of the steps above set targets, requirements, and expectations BEFORE you make the measurement. These should come from the data sheets, general physical considerations and the specifics of your application.
Don't even look at any real measurement data until you have proven that your setup does indeed measure vibration with sufficient accuracy and signal to noise ratio over the required frequency range and dynamic range. If that all checks out and you still see unexpected data you can ask again.