
Samsung Galaxy Fame
The latest firmware for Samsung Galaxy Fame (GT-S6810E) is S6810EUHAML1 with Jelly(Android Bean), released on May 7, 2014 for 1 region (CSC). Every official firmware build for GT-S6810E, 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/S6810EUHAML1

GT-S7508

GT-S7500T

GT-S6812

GT-S6500L

GT-S5690L

GT-S5670

GT-S5570I

GT-S5303
You can find the firmware on the model: GT-S6810E page.
Yes, all firmware files for GT-S6810E are 100% official, original, and obtained directly from Samsung servers.
To flash GT-S6810E, 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 GT-S6810E.