
Samsung Galaxy Tab3
The latest firmware for Samsung Galaxy Tab3 (SM-T310) is T310UEUCOI1 with Android 4.4.2 (KitKat), released on August 31, 2015 for 1 region (CSC). Every official firmware build for SM-T310, 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/T310UEUCOI1
All 35 builds in our database run Android 4.4.2 (KitKat). The newest build, T310UEUCOI1, was released on August 31, 2015. No new build has appeared for 135 months, so regular updates for this model have most likely ended.
Box codes of SM-T310 for different colors and markets. Firmware is chosen by the model code SM-T310 and your region (CSC), not by the SKU.

SM-T310X

SM-T210L

SM-T320X

SM-T321

SM-T307U
The newest firmware for SM-T310 runs Android 4.4.2 (KitKat): build T310UEUCOI1, released on August 31, 2015.
The latest build for SM-T310, T310UEUCOI1, was released on August 31, 2015 (11 years ago).
SM-T310 has had no new firmware for 135 months, so regular updates have most likely ended.
Yes, all firmware files for SM-T310 are 100% official, original, and obtained directly from Samsung servers.
To flash SM-T310, 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-T310.