https://play.google.com/store/apps/details?id=air.com.d20studios.heromages&feature=also_installed#?t=W251bGwsMSwxLDEwNCwiYWlyLmNvbS5kMjBzdHVkaW9zLmhlcm9tYWdlcyJd
This is a good game, and it's the closest you'll get to a tabletop board game. There's no real quest mode, the meat of the game is the battles, both online and offline, so see if that's your kind of game. There's an iOS thread, and you can try the game for free on your browser, so if this sounds like your kind of thing, you can't go wrong. You can think of it as a more tabletop version of Summoner Wars, with two warrior units on your team, and a summoner who can cast spells or summon magic creatures to fight for you. There are several unit types, which you can mix and match. Quite good fun - definitely it was the async multiplayer game I played on the go, even though the turns are a bit longer, and the notifications were by email at the time, which was a minor gripe.
