We study the percolation properties for a system of functionalized colloids on patterned substrates via Monte Carlo simulations. The colloidal particles are modeled as hard disks with three equally-distributed attractive patches on their perimeter. We describe the patterns on the substrate as circular potential wells of radius $R_p$ arranged in a regular square or hexagonal lattice. We find a nonmonotonic behavior of the percolation threshold (packing fraction) as a function of $R_p$. For attractive wells, the percolation threshold is higher than the one for clean (non-patterned) substrates if the circular wells are non-overlapping and can only be lower if the wells overlap. For repulsive wells we find the opposite behavior. In addition, at high packing fractions the formation of both structural and bond defects suppress percolation. As a result, the percolation diagram is reentrant with the non-percolated state occurring at very low and intermediate densities.
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