In April 1430, King Sejong sent officials to Hamgil and Kangwon provinces to find a rumored island named "Yodo." More than six months later, on October 23, there is a record that said that the governors of Hamgil and Kangwon provinces were instructed to send people to search for Yodo and were given directions where to look. The record also reported that the four people that the Hamgil governor sent to find Yodo found what appeared to be an island due south of Cape Muji, which was in the area of Gilju. Here is the record:
Source:『世宗實錄』 卷 五十, 世宗 十二年 十月 庚寅條The above record implies that King Sejong had heard that Yodo was located somewhere south of Cape Muji in Hamgil Province and north of Dang Mountain, which was near Tongcheon in Gangwon Province. Cape Muji was probably just north of present-day Kimcheak City in North Hamgyeong Province, and since Dang Mountain was reported to be near Tongcheon, it would be in the North Korean part of Gangwon Province.
October 23, 1430
先是傳旨于江原咸吉道監司曰 今所訪蓼島 在襄陽府靑臺上 通川縣堂山登望 則見于子丑間在 吉州無時串 洪原縣蒲靑社望見 則見于巳午間 基今詳明勤恪人 望見以聞 至是 咸吉道監司報 今殿直田闢等四人 往無時串 登望海中 有東西二峯 如島嶼 一微高 一差小 中有一大峯 立標測之 正當巳午間 遂送闢于京.
이보다 앞서 강원도와 함길도의 감사에게 교지를 내리기를,“지금 조사하려는 요도(蓼島)가 양양부(襄陽府)의 청대(靑臺) 위에서나 통천현(通川縣)의 당산(堂山)에 올라가서 바라보면 북쪽에 있고, 길주(吉州)의 무시곶[無時串]에서와 홍원현(洪原縣)의 포청사(蒲靑社)에서 바라보면 남쪽에 있으니, 자상하고 부지런하며 진실한 사람으로 하여금 바라보고 보고하게 하라.”하였는데, 이 때에 함길도 감사가 보고하기를,“전직(殿直) 전벽(田闢) 등 네 사람을 시켜서 무시곶에 가서 올라가 바다 가운데를 바라보니, 동쪽과 서쪽의 두 봉우리가 섬처럼 생겼는데, 하나는 약간 높고 하나는 약간 작으며, 중간에는 큰 봉우리 하나가 있는데, 표를 세워서 측량하여 본즉 바로 남쪽에 해당합니다.” 하니, 곧 전벽(田闢)을 서울로 보냈다.
The following instructions came after previous intructions to the governors of Gangwon and Hamgil Provinces: "If you go to the top of Cheongdae in the Yangyang district or to the top of Dang Mountain in Tongcheon and look out, the Yodo you are investigating will be to the north. If you look out from Cape Muji in Gilju or from Pocheongsa in Hongwon-hyeon, the island will be to the south. Have a diligent, attentive, and trustworthy people go look and report." The Hamgil governor reported, "I sent four people, including Jeon-jik and Jeon-byeok, to Cape Muji and had them climb up and look out into the middle of the sea. There were two peaks, one to the east and one to the west that looked like an island. One peak was a little smaller than the other. In the middle, there was one large peak. When a marker was set and a measurement taken, the island was reported to be due south." Jeon-byeok was immediately sent to Seoul.
If Yodo was north of Tongcheon, as King Sejong presumed, that would mean that neither Ulleungdo nor Dokdo/Takeshima could not have been Yodo, since they are southeast of Tongcheon. Also, it is unlikely that the island spotted by the people at Cape Muji was Ulleungdo or Dokdo/Takeshima since Cape Muji was in what today is North Hamgyeong Provice, which is almost certainly too far away to see even Ulleungdo.
I suspect that the people at Cape Muji were just reporting what they thought King Sejong wanted hear because there are no islands due south of where they were. Or maybe they spotted peaks on the mainland in Gangwon Province and presumed them to be part of an island? Whatever they spotted, it was not an island since there are no islands due south of Kimchaek City.