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Thats my question.
Yes, this way are:

1. Install Xpadder (in my case 5.3)
2. Xbox One Controller
3. Windows 7.64

That's my answer.
At a general level, DOSBox supports game controllers, like Ye Olde HID Gamepad - exposes them to the games inside. So for every game, the question is if and how the game is coded to work with controllers. Good news here: both AB and AB:TA support them!

For Alien Breed: there is no way to just start using your gamepad in the game. You need to run CONFIG.EXE first. You probably won't be able to do that directly, but the DOSBox wrapper was prepared for you, under "Launch Settings.lnk". In there you can rebind keys (Backspace? seriously?!) or choose "joystick", then mash some directions and save the settings.

For Tower Assault: a gamepad/joystick will work right away in the menu. You can use it to change "CONTROL TYPE" to "JOYSTICK". But there is a catch: while the game could potentially be an enjoyable experience with a gamepad even in the year 20XX, it was coded when joysticks had one or two buttons at most. So you'll fire using button #0, and switch to that good-intentioned-but-oh-so-awkward retreat mode using button #1 (it will be another decade until twin-stick is the standard). That secondary button will also activate Intex consoles and display map, after you hold it for ~1s.

So far so good, right? I don't even mind that delayed map. So what's wrong? Well, the weapon selection is very much missing from the controls, so you'll need to reach the keyboard for that (F5? seriously?!). If there is another way, I never found it. Having pause on the gamepad would also be nice. So yeah, if it impacts the experience for you just like it did for me, maybe you oughta install Xpadder or something similar, and just bind the pad buttons to keys the game understands.

Hope this helps someone who couldn't get their gamepad to work with TA!