
Samsung Galaxy Note3 Duos
The latest firmware for Samsung Galaxy Note3 Duos (SM-N9002) is N9002ZNUGPA1 with Android 5.0 (Jelly), released on January 4, 2016 for 1 region (CSC). Every official firmware build for SM-N9002, newest first: one row per build with all regions (CSC) that received it.
SM-N9002 started on Android 4 and has received 1 major Android upgrade; it now runs Android 5.0 (Jelly). The newest build, N9002ZNUGPA1, was released on January 4, 2016. No new build has appeared for 131 months, so regular updates for this model have most likely ended.
Specifications of SM-N900, a regional variant of the same device. Chipset and SIM lines are left out: they can differ by region.

SM-N920AZW

SM-N920VZW

SM-N950UZK

SM-N920AZK

SM-N950X

SM-N930V

SM-N9300

SM-N930S
The newest firmware for SM-N9002 runs Android 5.0 (Jelly): build N9002ZNUGPA1, released on January 4, 2016.
The latest build for SM-N9002, N9002ZNUGPA1, was released on January 4, 2016 (10 years ago).
SM-N9002 has had no new firmware for 131 months, so regular updates have most likely ended.
Yes, all firmware files for SM-N9002 are 100% official, original, and obtained directly from Samsung servers.
To flash SM-N9002, 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-N9002.