Quad Touch is widely regarded as the gold standard for mobile Quake ports due to its robust feature set:
The Ultimate Guide to Quad Touch APK: Play Classic Retro Shooters on Android
Copy your id1 (Quake 1), baseq2 (Quake 2), or baseq3 (Quake 3) folders from your PC to your phone's internal storage.
Connect your phone to your computer via USB or use an Android file manager app.