Tinytouchtales makes really good mobile strategy games with some puzzle like elements. I think all of their games are free to try with a purchase to unlock the full game. Card Crawl and Card Thief are the most popular. I think Card Crawl and Miracle Merchant are good ones to try since they are maybe a bit easier to learn. A few of their games are a little more complicated like Card Thief and Card Crawl Adventure but I recommend those too. Geo Gods is their newest which I also recommend if you like the others.
I also really like Golf Peaks and Inbento created by Afterburn. I think both cost 2.99 USD. They both have a finite number of puzzles to complete and are easy to learn but hard to finish.
Zhed is a good free puzzle game. I think it has IAP for hints.
Broki is another good free one with ads. IAP for ad removal and hints.
Small Islands is a completely free puzzle game with no ads that I would recommend.
Hope you find something here you like!