National Korean health insurance
Since 2019.07.16 the Korean government included F-4 visa holders to contribute for their National health insurance system.
That means that current F-visa holders and for adoptees that applying for their F-4 visa will be automatically enrolled for National healthcare.
Currently the contribution per month is around 123,080 won (depends on your situation for example if you have property, a car etc. the amount could be possibly increased).
If you are staying longer than 6 months in Korea you will receive a white envelope with H-well on it.
H-well is the National health insurance company (below a link to their website)
In picture 1 you can see the envelope that you can expect at your registered address in South-Korea after a 6 month stay.
Be aware that if you are living for more than 6 months in Korea before 2019.07.16 and you didn't pay the bills from that date until now, the immigration office has reasons to decline your extension for you F-4 visa!
In picture 2 you can see a more detailed bill were you can find the total amount for your health insurance.
You also receive an insurance card in case you need to visit the doctor or dentist to show your health insurance number. Usually if you work your company pays 50% of the medical bills and you pay 50%.
Picture 1 The envelope from your health insurance
Picture 2 The detailed bill from your health insurance