I have never seen any written statement, but so far I have learned and experienced the below.
Through GATE (Graduate Aptitude Test in Engineering) score, you can take admission for PhD program with 25k p.m. scholarship in
IITs/NITs (Indian/National Institute of Technology),
IISc (Indian Institute of Science),
IISERs/NISERs (Indian/National Institute of Science Education and Research)
and some other Institutes in India.
Through GATE, you can also take admission into PhD program with about 2000 SGD p.m. scholarship in
NUS (National University of Singapore)
and NTU (Nanyang Technological University, Singapore).
To answer your question:
If I only have a valid GATE score but no CSIR-JRF NET qualification,
will I be eligible for the 25 k funding?
Yes, but not everywhere. Please visit the webpage of the Institutes/Universities and check their instructions about scholarship or inquire via telephone or email.
If yes to above, is this funding available for any NAAC-accredited
university (public or private) in India?
Not sure, may be available, but very limited.
Is there any written statement from the government which validates
I have never searched such written statements.