The current paper presents a determination of K^0_SK S0 and \Lambda/\bar{\Lambda}Λ/ Λ ˉ fragmentation functions (FFs) from QCD analysis of single-inclusive electron-positron annihilation process (SIA). Our FFs determinations are performed at next-to-leading order (NLO), and for the first time, at next-to-next-to-leading order (NNLO) accuracy in perturbative Quantum Chromodynamics (pQCD) which is designated as {\tt SAK20} FFs. Each of these FFs is accompanied by their uncertainties which are determined using the `Hessian' method. Considering the hadron mass corrections, we clearly investigate the reliability of our results upon the inclusion of higher-order QCD correction. We provide comparisons of {\tt SAK20} FFs set with the available analysis from another group, finding in general a reasonable agreement, and also considerable differences. In order to judge the fit quality, our theoretical predictions are compared with the analyzed SIA datasets. {\tt SAK20} FFs at NLO and NNLO accuracy along with their uncertainties are made available in the standard {\tt LHAPDF} format in order to use for predictions of present and future measurements in high-energy collisions such as LHC and RHIC.