We have carried out an X-ray study of a deeply embedded Wolf-Rayet star WR 121a using long-term (spanning over ~12 years) archival observations from Chandra and XMM-Newton. For the first time, a periodic variation has been seen in the X-ray light curves of WR 121a corresponding to a period of 4.1 +/- 0.1 days. No companion is seen in a merged and exposure corrected Chandra X-ray image of WR 121a as shown in the other previous studies. The X-ray spectrum of WR 121a has been well-explained by a thermal plasma emission model with temperatures of 0.98 +/- 0.34 keV and 3.6 +/- 0.7 keV for the cool and hot components, respectively with non-solar abundances. The present study indicates that X-rays WR121a is one of the X-ray bright massive binaries with an X-ray luminosity of ~10^{34} erg/s, where the X-ray are mainly produced by an active wind collision between its components. The phase-locked modulations have been seen in the flux variation of WR 121a where the flux is increased by a factor of ~1.7 from minimum to maximum in 0.3-10.0 keV energy band. These variations could be caused by an eclipse of the wind collision region by the secondary star in a binary orbit. The winds of both the components of WR 121a are suspected to be radiative during all the times and processes like radiative inhibition as well as braking are most likely affecting the wind collision severely in this short period massive binary system.