There isn't one single "correct" way to spell Joseph in Korean, as the romanization of names can vary depending on the chosen system and personal preference. However, the most common and natural-sounding spellings would be:
* 요셉 (Yosep): This is a very common and accepted transliteration.
You might also occasionally see other spellings, but they would be less common and might sound less natural to a Korean speaker. Yosep is your best bet.