I see water dripping from the water valve, but when I feel the valve, no water residue is detected. Where can this drip be coming from?

The first option could be a leak from the toilet fill valve base. The seal in the tank under the fill valve may be loose or worn. Hand-tightening the plastic nut under the tank for the fill valve may re-seal it. Otherwise, a new fill valve can be installed (with a new seal). It could also be a leaking source valve. Either tighten the seal nut on the valve shaft or back the valve all the way open to seal the valve shaft. The third option could be humidity condensation. Add an insulation cover to the toilet tank to prevent condensation. Some systems use a portion of hot water for the tank refill to warm it enough to prevent condensation, and in such setups the hot water valve portion could be opened more.