Samsung Galaxy J3 (2016)
The latest firmware for Samsung Galaxy J3 (2016) (SM-J320A) is J320AUCU3BVH1, released on June 20, 2023 for 1 region (CSC). Every official firmware build for SM-J320A, 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/J320AUCU3BVH1
The newest build, J320AUCU3BVH1, was released on June 20, 2023. No new build has appeared for 40 months, so regular updates for this model have most likely ended.
Specifications of SM-J320F, a regional variant of the same device. Chipset and SIM lines are left out: they can differ by region.

SM-J320VPP

SM-J327VPP

SM-J326AZ

SM-J337A

SM-J330N
The latest build for SM-J320A, J320AUCU3BVH1, was released on June 20, 2023 (3 years ago).
SM-J320A has had no new firmware for 40 months, so regular updates have most likely ended.
Yes, all firmware files for SM-J320A are 100% official, original, and obtained directly from Samsung servers.
To flash SM-J320A, 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-J320A.