
Samsung Galaxy Tab E 8.0
The latest firmware for Samsung Galaxy Tab E 8.0 (SM-T377P) is T377PVPU3CQI4 with Android 7.1.1 (Marshmallow), released on September 10, 2017 for 2 regions (CSC). Every official firmware build for SM-T377P, 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/T377PVPU3CQI4
SM-T377P started on Android 6 and has received 1 major Android upgrade; it now runs Android 7.1.1 (Marshmallow). The newest build, T377PVPU3CQI4, was released on September 10, 2017. No new build has appeared for 111 months, so regular updates for this model have most likely ended.
Box codes of SM-T377P for different colors and markets. Firmware is chosen by the model code SM-T377P 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-T377P runs Android 7.1.1 (Marshmallow): build T377PVPU3CQI4, released on September 10, 2017.
The latest build for SM-T377P, T377PVPU3CQI4, was released on September 10, 2017 (9 years ago).
SM-T377P has had no new firmware for 111 months, so regular updates have most likely ended.
Yes, all firmware files for SM-T377P are 100% official, original, and obtained directly from Samsung servers.
To flash SM-T377P, 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-T377P.