This work investigates numerically the influence of electroosmotic vortex produced by positively charged patches on the reaction characteristics of two species A and B. By altering the patch zeta potential ratio and relative concentration of species B, the flow field, product concentration field, recirculation strength, product concentration flow rate, and production rate are evaluated. It is found that the generation of maxima concentration of species C (CC) is higher for the non-uniformly charged case, as well as, the prediction of maxima CC started more toward the upstream for the non-uniformly charged micro-reactor compared to the uniformly charged case. Additionally, patch zeta potential increases recirculation strength while decreasing product concentration flow rate. Up to a critical point, the production rate increases with a relative concentration increase of species B, after which it becomes insensitive. Moreover, the non-uniformly charged micro-reactor gives a higher production rate at a higher relative concentration of species B compared to the uniformly charged case. The results of the current study can be utilized to improve the design of micro-reactors used in the chemical and biological sectors.