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There's a decent port of Battle for Wesnoth, but it kind of requires a large tablet, and I wasn't a fan of how the controls were implemented (essentially mouse simulation). That said, the game itself is a hex-based tactics game played in a typical "humans in a middle age fantasy setting", so quite similar to BB.
I honestly recommend you turn-based games on mobile, rather than real-time games like Age of Empires. That's because your input on mobile devices may often be hindered by various circumstances. A real-time game requires a lot of precision and quickness, so you won't be able to risk playing it while standing up in the subway and playing with one hand only, for example. I'm a fan of various RTS games on PC, but on mobile I found myself most inclined to play simpler turn-based strategy games. As an example: Battle for Wesnoth , or even the simple rogue-like Hoplite. Those are more tactical games than strategy games (no direct resource gathering), but there are actually some RPG resources, so to say, that you would find yourself "harvesting" at times, and also the tactical decisions can be surprisingly challenging and entertaining for you as an RTS fan who likes similar thrill on mobile.
Closest I can think of are Braveland series (3 I think?) and Battle for Wesnoth
LinkMe: Braveland
https://play.google.com/store/apps/details?id=com.androthsoft.battle&hl=en
Battle for Wesnoth, a classic, easy to learn, hard to master.