Epitaxial $Ba_{0.5}Sr_{0.5}TiO_3$ (BSTO) thin films have been grown on TiN buffered Si (001) substrates by Pulsed Laser Deposition (PLD) method and the effects of substrate temperature and oxygen partial pressure during the deposition on their dielectric properties and crystallinity were investigated. The crystal orientation, epitaxy nature, and microstructure of oxide thin films were investigated using X-Ray Diffraction (XRD) and Transmission Electron Microscopy (TEM). Thin films were prepared with laser fluence of $4.2;J/cm^2;and;3;J/cm^2$, repetition rate of 8 Hz and 10 Hz, substrate temperatures of $700^{circ}C$ and ranging from $350^{circ}C;to;700^{circ}C$ for TiN and oxide respectively. BSTO thin-films were grown on TiN-buffered Si substrates at various oxygen partial pressure ranging from $1{ imes}10^{-4}$ torr to $1{ imes}10^{-5}$ torr. The TiN buffer layer and BSTO thin films were grown with cube-on-cube epitaxial orientation relationship of $[110](001)_{BSTO}{parallel}[110](001)_{TiN}{parallel}[110](001)_{Si}$. The crystallinity of BSTO thin films was improved with increasing substrate temperature. C-axis lattice parameters of BSTO thin films, calculated from XRD ${ heta}-2{ heta}$ scans, decreased from 0.408 m to 0.404 nm and the dielectric constants of BSTO epitaxial thin films increased from 440 to 938 with increasing processing oxygen partial pressure.