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zxtune plays most common module formats and emulates some chip hardware formats like c64's SID and Sega Mega Drive's yamaha YM2612
https://play.google.com/store/apps/details?id=app.zxtune&hl=en_AU&gl=US
Plus you can browse AMP with it

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facepalm, here's me not reading properly.

• Sunvox can open .MOD and .XM modules, but it's as much a modular audio synthesis tool as it is a tracker. Can't export to MOD or XM though, only to its native SVOX module format.
  
• There's also an unofficial and maybe unsupported? port of MilkyTracker for Android. it's outdated, throws a bunch of errors when you first run it on later versions of Android, but it seems to work normally for me. your mileage may vary.
  

Not a lot of android-native options - trackers are VERY keyboard-centric so the touchscreen is a big disincentive. That said, if you get yerself a bluetooth keyboard (i recommend rii's mini bluetooth ones. they've got nice clicky buttons instead of rubber calculator-style ones. A mechanical keyboard it ain't, but) then you can mess around with emulating and using a tracker the way the good lord intended:

• If you're *nixy, you can download termux off f-droid.org and a vnc server. MilkyTracker is in their x11-apps repo and will maybe be more stable.
  
• or, you can dive down the wild rabbit hole of android amiga emulators and actually get protracker off aminet
  
• or or, you can download one of the Android dosbox ports,  magicdosbox is pretty active and has a free version you can try out. All the classics like fasttracker 2, screamtracker 3 etc, you can get off pouet.org. That's what I've been doing. I was too young to have owned an amiga, but now i can carry a 486 around in my pocket.

Thank you for coming to my ted talk.