Cat peeing on my clean and dirty clothes.?

My cat is 2 years old and ever since I got him he's peed on my clothes/linens. It started off as litter training and once we got that down he's been good. When I moved he would only pee on the dirty clothes or the ones that have been sitting out and not put away for more than a few days. Now he continues to do it and I took him to the vet and they said nothing was wrong with him. I've tried changing the litter and making him stay in the same room for a while and even tried that "calm" plug in and nothing has helped. I am running out of ideas and patience. I keep getting told to get rid of him and put him to sleep but he's my baby and I could never do it (may have thought of that on my most stressful days though). Someone please help me or give me some new ideas to try.