I wouldn't consider under 15-20 minutes a proper nap. I would say it is an indication that baby is exhausted and struggling to go to sleep easily.
Not unusual for naps in the newborn (under 3 month old) to be long, a couple of hours. This is actually the 'easy' stage for naps. They get much more difficult after 3 ish months, when sleep needs a lot more work and form in sleep cycles.
I would suggest your baby sounds over tired and exhausted.
A well fed, well winded, swaddled under 3 month old with a dummy should sleep fairly easily and passively.
Are you swaddling? It helps baby feel safe and secure, like in the womb.
Are you giving a dummy? Babies are naturally programmed to find sucking soothing and calming, it mimics breastfeeding.
Then try gently swaying the swaddled baby with a dummy. Nothing vigorous. It's recreating the swishing around feeling from in the womb.
When putting down for a nap, keep the weight of your body on baby's. So bend at the waist and keep baby in position next to you, so you hover above baby as they are laid down. Put your hand, spread wide, quite firmly on baby's chest as they are laid down and stay there until settled. Baby is reassured by feeling you close.
Then feeding. The vast majority of sleep issues in the under 3 month old is likely to be caused by feeding and/or winding.
A hungry baby just isn't going to go to sleep. A baby who's calorie intake is on the low side overall (over 24/48 hours) is likely to be a lighter sleeper, waking more easily.
A baby with wind will be either uncomfortable or outright in pain so is not going to sleep well. Adequate winding is very important. There are lots of different winding methods are online.