A Catalog of Periodic Variables in Open Clusters M35 and NGC 2158

We present a catalog of 1143 periodic variables, compiled from our image-subtracted photometric analysis of the K2 Campaign-0 super stamp. This super stamp is centered on the open clusters M35 and NGC 2158. Approximately 46% of our periodic variables were previously unreported. Of the catalog variables, we find that 331 are members of M35 and 56 are members of NGC 2158 ( ${P}_{{\rm{m}}}\,\gt \,0.5$ ). Our catalog contains two new transiting exoplanet candidates, both of which orbit field stars. The smaller planet candidate has a radius of 0.35 ± 0.04 ${R}_{{\rm{J}}}$ and orbits a K dwarf ( ${K}_{{\rm{p}}}$ = 15.4 mag) with a transit depth of 2.9 millimag. The larger planet candidate has a radius of 0.72 ± 0.02 ${R}_{{\rm{J}}}$ and orbits a late G-type star ( ${K}_{{\rm{p}}}$ = 15.7 mag) with a transit depth of 2.2 millimag. The larger planet candidate may be an unresolved binary or a false alarm. Our catalog includes 44 eclipsing binaries (EBs), including ten new detections. Of the EBs, one is an M35 member and five are NGC 2158 members. Our catalog contains a total of 1097 nontransiting variable stars, including a field δ Cepheid exhibiting double mode pulsations, 561 rotational variables, and 251 pulsating variables (primarily γ Doradus and δ Scuti types). The periods of our catalog sources range between 43 minutes to 24 days. The known ages of our reported cluster variables will facilitate investigations of a variety of stellar evolutionary processes.