The wetting behavior of rock/CO₂/brine systems highly impacts the fluid distribution at the pore-scale and multiphase flow at the macroscale and is considered a key parameter controlling the CO₂ residual trapping in geological storage. The effect of wettability on residual trapping is, however, still uncertain as the current literature suggests high discrepancies among the published datasets. Moreover, the dataset for residual trapping observations for non water-wet carbonate rocks is relatively scarce; none of the published studies investigated this aspect in CO₂-wet limestones. Thus, a series of core-flooding experiments was conducted at reservoir conditions for three limestone samples having different wettability states, water-wet, intermediate wet, and CO₂-wet. Wettability alteration of sister rocks was achieved using stearic acid to mimic the wettability alteration in saline aquifers due to the interaction with natural organic compounds. Notably, increasing the hydrophobicity of limestone tends to decrease CO₂ residual trapping efficiency $\sim$ 19% and 37% when the initial water-wetting state shifts to intermediate-wet and CO₂-wet, respectively. This is attributed to the fluid distribution at the pore scale, in particular the wetting layers, and its effect on the CO₂/brine displacement. In case of CO₂-wet rocks, macroscopic CO₂-wetting layers act as flow paths, which reduces the residual CO₂ saturation from 29% (water-wet) to 8%. These findings advocate water-wet rocks as better candidates for CO₂ residual trapping and provide insights into residual trapping-rock wettability correlation pertinent to CO₂ geo-storage.