
Samsung Galaxy S4 (Korea/KTF)
The latest firmware for Samsung Galaxy S4 (Korea/KTF) (SHV-E300K) is E300KKTUGPI1 with Android 5.0.1 (Lollipop), released on September 18, 2016 for 1 region (CSC). Every official firmware build for SHV-E300K, newest first: one row per build with all regions (CSC) that received it.
Each firmware build has its own page at https://samfirm.shop/build/{PDA}, where {PDA} is the build number from the list above. Example: https://samfirm.shop/build/E300KKTUGPI1
SHV-E300K started on Android 4 and has received 1 major Android upgrade; it now runs Android 5.0.1 (Lollipop). The newest build, E300KKTUGPI1, was released on September 18, 2016. No new build has appeared for 122 months, so regular updates for this model have most likely ended.

SHV-E500L

SHV-E400K

SHV-E370K

SHV-E330L

SHV-E330K

SHV-E310L

SHV-E310K

SHV-E300L
The newest firmware for SHV-E300K runs Android 5.0.1 (Lollipop): build E300KKTUGPI1, released on September 18, 2016.
The latest build for SHV-E300K, E300KKTUGPI1, was released on September 18, 2016 (10 years ago).
SHV-E300K has had no new firmware for 122 months, so regular updates have most likely ended.
Yes, all firmware files for SHV-E300K are 100% official, original, and obtained directly from Samsung servers.
To flash SHV-E300K, you need to download the appropriate firmware, put your device into Download Mode, and use the Odin tool to load the BL, AP, CP, and CSC files.
Downgrading is only possible if the bootloader version (binary bit) of the old firmware matches the current one. Always check the binary version before flashing SHV-E300K.