I feel your pain - I had this with both my children. Second one in particular was a nightmare for it. I think I had time with first to soothe him back to sleep when he woke but with her there was no time so she just had to get up. I went by the 90 minute rule and put her down 90 minutes from when she woke up which in theory meant at least that she didn't get over-tired. It meant some days she was having 5 naps!!
FWIW she is now 2.5 years old and would nap for 2 hours if I let her. She got to about 7 months I seem to remember (or maybe later) and started doing longer napping.
After around 20 minutes of falling asleep the baby's sleep normally changes from REM to a deep sleep stage. At that point they either stir and wake up or are able to transition into the deeper sleep stage. That might explain why your LO is waking up after 20 mins into the nap. If you google babies' sleep cycles you'll find more info.. Basically, babies have shorter sleep cycles (45 mins as opposed to the adults' 90 mins) and they go into the REM sleep stage first before falling into deep sleep unlike adults, who first fall into deep sleep which is followed by REM.
My 16 weeks old is exactly the same - at day time would not resettle after 20 min despite the yawns and being obviously still tired. He would not go over 20min even in my arms, only occasionally outside in a pram. But even that not everyday. Just hope he'll grow out of that - it is so tiring. He also stopped sleeping at nights, poor thing. Does not look like a wind or any physical problem. sorry cannot help, but would love to find a solution myself! On rare occasions when he sleeps longer, he is so much happier in the evenings!
Do you feed to sleep? Only whenever DD used to wake up after 20 minutes it was wind... If not, could you try being right there when he wakes at the 20-min mark to shush/pat/stroke him and/or stop his arms flailing about when he wakes?
But I would try not to let it stress you put too much. Babies go through a lot of developmental stuff at this age, which can cause disruption - Google 4-month sleep regression for more info.
If he's crying in his cot then he's not sleeping either - I personally wouldn't leave him to cry. If you can't get him to settle again by sshing him or whatever then as you say, try again later.
However, I found at that age DD really didn't sleep well in her cot during the day. She would do a max of 20 mins in the cot, but well over an hour in the sling, or as she got older, the buggy. I seem to recall at four months all our naps were in the sling, at 5 months they were in the buggy, but me having to walk with it to keep her asleep, and by 6 months (ish) she was napping in the buggy and staying asleep after it being rocked for a bit.
She still takes all her naps in her buggy at 10mo and has an hour in the morning and 2 hours in the afternoon. As she sleeps so well in it I haven't had any reason to try to get her to nap in her cot again really.
I am really struggling with my 4mth olds sleep in general and have posted on it before, but I've got a specific question on what to do when he wakes after just 20mins during the day. Should I leave him in his cot crying, or just give in and try again later? Yesterday he had about an hour of sleep throughout the day in 3 different sessions.