
Samsung Galaxy Note
The latest firmware for Samsung Galaxy Note (GT-I9220) is I9220ZCLSG with Jelly(Android Bean), released on August 2, 2013 for 1 region (CSC). Every official firmware build for GT-I9220, 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/I9220ZCLSG

GT-I9308

GT-I9268

GT-I9228

GT-I9210

GT-I9108
You can find the firmware on the model: GT-I9220 page.
Yes, all firmware files for GT-I9220 are 100% official, original, and obtained directly from Samsung servers.
To flash GT-I9220, 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-I9220.