
The latest firmware for GT-S5301B is S5301BVJAMK1 with Android 4.0.4 (Ice Cream Sandwich), released on September 30, 2014 for 1 region (CSC). Every official firmware build for GT-S5301B, 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/S5301BVJAMK1

GT-S7508

GT-S6812

GT-S6500L

GT-S5690L

GT-S5670
You can find the firmware on the model: GT-S5301B page.
Yes, all firmware files for GT-S5301B are 100% official, original, and obtained directly from Samsung servers.
To flash GT-S5301B, 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-S5301B.