
Samsung Galaxy S4 (TD-LTE)
The latest firmware for Samsung Galaxy S4 (TD-LTE) (GT-I9507) is I9507XXUHOJ1 with Android 5.0.1 (Lollipop), released on October 15, 2015 for 1 region (CSC). Every official firmware build for GT-I9507, 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/I9507XXUHOJ1
GT-I9507 started on Android 4 and has received 1 major Android upgrade; it now runs Android 5.0.1 (Lollipop). The newest build, I9507XXUHOJ1, was released on October 15, 2015. No new build has appeared for 134 months, so regular updates for this model have most likely ended.

GT-I9308

GT-I9268

GT-I9228

GT-I9210

GT-I9108

GT-I9103

GT-I9100T

GT-I9050
The newest firmware for GT-I9507 runs Android 5.0.1 (Lollipop): build I9507XXUHOJ1, released on October 15, 2015.
The latest build for GT-I9507, I9507XXUHOJ1, was released on October 15, 2015 (11 years ago).
GT-I9507 has had no new firmware for 134 months, so regular updates have most likely ended.
Yes, all firmware files for GT-I9507 are 100% official, original, and obtained directly from Samsung servers.
To flash GT-I9507, 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-I9507.