
Samsung Galaxy Tab4 10.0
The latest firmware for Samsung Galaxy Tab4 10.0 (SM-T535) is T535XXS1BRJ2 with Android 5.0.2 (Lollipop), released on October 29, 2018 for 10 regions (CSC). Every official firmware build for SM-T535, 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/T535XXS1BRJ2
SM-T535 started on Android 4 and has received 1 major Android upgrade; it now runs Android 5.0.2 (Lollipop). The newest build, T535XXS1BRJ2, was released on October 29, 2018. No new build has appeared for 97 months, so regular updates for this model have most likely ended.
Box codes of SM-T535 for different colors and markets. Firmware is chosen by the model code SM-T535 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-T535 runs Android 5.0.2 (Lollipop): build T535XXS1BRJ2, released on October 29, 2018.
The latest build for SM-T535, T535XXS1BRJ2, was released on October 29, 2018 (7 years ago).
SM-T535 has had no new firmware for 97 months, so regular updates have most likely ended.
Yes, all firmware files for SM-T535 are 100% official, original, and obtained directly from Samsung servers.
To flash SM-T535, 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-T535.