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I used to read the Journal of Recreational Mathematics (JRM) when I was in college at Michigan State. After college, I would visit the Math Library there and take out issues with my still-good library card. Later on, I subscribed to the periodical at four issues a year, for $18.00 plus shipping as I recall. Years ago I donated all the issues I had - perhaps five or ten years worth - to either a local school or my local library. What I recall most about the JRM was the puzzles they had - I was totally uninterested in alphametics like SEND + MORE = MONEY, but others appealed to me.

Another small addition:

Maths Week England

2022
https://mathsweekengland.co.uk/?page_id=7470

2021
https://www.youtube.com/channel/UCUGTfib...YBA/videos

Another small addition. There are conferences in honor of Martin Gardner and some parts are on youtube in underrated channels.

https://www.youtube.com/@G4GCelebration/videos
(more info: https://en.wikipedia.org/wiki/Gathering_4_Gardner )

I discovered this through this video: https://www.youtube.com/watch?v=zsN2AiZWBus (another underrated channel, but it is not about recreational mathematics)

Not strictly a periodical, but a collection of problems (though there are some sites about those, like project euler, art of problem solving and so on): https://ukmt.org.uk/current-past-papers/