Broadband Variability Analysis of FSRQ PKS\,0402-362 with Indications of Quasi-Periodic Modulation

We present a comprehensive temporal and spectral study of the flat-spectrum radio quasar PKS~0402$-$362 using \textit{Fermi}-LAT/Swift-XRT/UVOT observations spanning from MJD 54686-60321. The $γ$-ray light curve exhibits multiple phases of enhanced activity, with the fractional variability parameter ($F_{\mathrm{var}}$) showing larger amplitudes at longer timescales, consistent with variability trends observed in other FSRQs. Statistical analysis of the flux and spectral index distributions using the Anderson--Darling test and histogram fitting reveals that both distributions deviate from a single log-normal form and are better represented by a double log-normal profile, indicating two distinct flux states. A search for quasi-periodic oscillations in the $γ$-ray emission using the Lomb--Scargle periodogram identified a significant periodic signal at $\sim$413~days with a confidence level exceeding $3σ$. However the proximity of the timescale to one year and limited number of observed cycles prevents a definitive interpretation. Broadband spectral energy distributions for six flux states were modeled using a one-zone leptonic framework incorporating synchrotron, synchrotron self-Compton (SSC), and external Compton (EC) components. The SEDs are well reproduced with physically reasonable parameters: high-flux states exhibit harder electron spectra and lower magnetic field strengths ($B \sim 0.2--0.6\,\mathrm{G}$), while low-flux states show softer spectra and stronger magnetic fields ($B \sim 1.3\,\mathrm{G}$). The fitted break energy decreases during high-flux states, suggesting enhanced radiative cooling and a transition toward a particle- or kinetic-energy-dominated jet. These trends are consistent with the ``harder-when-brighter'' behavior commonly observed in blazars.