After Effects is not changing the preview quality! I have the preview resolution set to quarter, frame skip set to 5 and yet After Effects is previewing at full resolution constantly. I have tried changing the settings through the sidebar and the bar under the preview.

I have purged the RAM, cache, etc. several times and even re-opening the program does not help.

The preview is indeed set to 'Adaptive resolution'. This is making the preview playback impossible since my footage is 4K.
Quarter of 4K is still 1080. Depending on your rig it still might chug thru playback. I would look into proxies as they are pretty quick to set up and would drastically improve workability.