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Relativistically energetic, non-thermal population of electrons can give rise to unique CMB spectral distortion signatures which can be significantly different from thermal Sunyaev-Zeldovich signal or $y$-distortion. These signatures depend upon the spectrum of non-thermal electrons, therefore, a detection can inform us about the existence and abundance of non-thermal electrons in our universe. Using public CMB maps and data, we derive upper limits on non-thermal $y$-parameter for a relativistic, power-law electron distribution. With future CMB experiments, we may be in a position to detect or put significantly tighter constraints on these signals which can affect our understanding of non-thermal electron distributions in our universe.