  Recently, the emergence of superconductivity in kagome metals has generated
significant interest due to its interaction with flat bands and topological
electronic states, which exhibit a range of unusual quantum characteristics.
This study thoroughly investigates largely unexplored breathing Kagome
structure C14 laves phase compounds XOs$_{2}$ (X = Zr, Hf) by XRD, electrical
transport, magnetization, and specific heat measurements. Our analyses confirm
the presence of the MgZn$_{2}$-type structure in ZrOs$_{2}$ and HfOs$_{2}$
compounds, exhibiting type-II superconductivity with critical temperature
(T$_{C}$) values of 2.90(3) K and 2.69(6) K, respectively. Furthermore,
specific heat measurements and an electron-phonon coupling constant suggest the
presence of weakly coupled BCS superconductivity in both compounds.
