I'm not sure an official manga adaptation exists yet, which is probably why you're struggling to find it! 'Under the Oak Tree' began as a web novel, and its popularity definitely sparked rumors about a comic version. From what I've seen floating around fan communities, there was talk of a manhwa adaptation, but I haven't stumbled upon any official, completed chapters from a licensed publisher. Sometimes these projects get announced and then take ages to materialize, or they might be region-locked on a Korean platform that's tough to access without specific payment methods.
Your best legal bet right now is actually the source material. The web novel is officially translated on platforms like Webnovel and Manta. Manta, in particular, has a subscription model that lets you read a ton of content, including 'Under the Oak Tree,' for a flat monthly fee. It's not the manga you wanted, but the story is all there. For actual comics, keep an eye on Tapas or Tappytoon—they're the big legal hubs for Korean manhwa. If an adaptation ever gets officially licensed, it'll almost certainly pop up there first.
Searching for free manga versions often leads to aggregator sites that use fan-scans without permission. Those sites are a legal gray area at best, and the translation quality can be wildly inconsistent, sometimes even switching halfway through a chapter. I'd rather re-read the novel on an official app and imagine the scenes than deal with that mess. The novel's descriptions are pretty vivid anyway.