>>It has been over a month and I have not received any replies
The pool here is pretty shallow. You're swimming by yourself. It's a 15 year old part design, the staff that designed / supported this are likely doing other things these days.
TM4C129EXL ? The code could probably do with using tables. I'm not sufficiently familar with the board design or MCU to confirm if the pin usage, or timing, nor what you're actually reading/writing into the MT48T201V.
You're not providing a dump of any of the RTC/Timing registers/memory locations
You'd need to select a frequency for the output RS3-RS0 (0x7FFF0), and enable via SQWE (0x7FFF6). Check you can read/write the registers successfully.
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