
Samsung Galaxy Tab4 8.0
The latest firmware for Samsung Galaxy Tab4 8.0 (SM-T337V) is T337VVRS3BPL1 with Android 5.1.1 (KitKat), released on December 6, 2016 for 1 region (CSC). Every official firmware build for SM-T337V, 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/T337VVRS3BPL1
SM-T337V started on Android 4 and has received 1 major Android upgrade; it now runs Android 5.1.1 (KitKat). The newest build, T337VVRS3BPL1, was released on December 6, 2016. No new build has appeared for 120 months, so regular updates for this model have most likely ended.
Box codes of SM-T337V for different colors and markets. Firmware is chosen by the model code SM-T337V and your region (CSC), not by the SKU.

SM-T290N

SM-T537A

SM-T800X

SM-T807V

SM-T230X

SM-T230NY

SM-T237V

SM-T232
The newest firmware for SM-T337V runs Android 5.1.1 (KitKat): build T337VVRS3BPL1, released on December 6, 2016.
The latest build for SM-T337V, T337VVRS3BPL1, was released on December 6, 2016 (9 years ago).
SM-T337V has had no new firmware for 120 months, so regular updates have most likely ended.
Yes, all firmware files for SM-T337V are 100% official, original, and obtained directly from Samsung servers.
To flash SM-T337V, 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 SM-T337V.