baby fights sleep

I have a 3 month old who I feel like barely naps. He naps for maybe 20-40 minutes every 4 hours. He won't take a good nap unless I'm holding him. Which he pretty much demands to be held all day. When he falls asleep on me and I lay him down he wakes up within 15 minutes and screams till I pick him up. When he is tired and I try to lay him down he just screams, kicks and refuses to sleep. At night he sleeps from 11pm- 5:30 am with out waking up, but that didn't start happening until I started letting him sleep with me in bed. Anything I could to help him nap during the day?