The sane way to approach it would be to develop a 3rd party library and make it available over the internet through open source, Github etc.
The GNU C dialect is one such example, which is a collection of non-standard compiler extensions used by the GCC compiler. One could join the GCC open source group and try to get the new function added there. It would still not be standard library C, but the GCC extensions are often an inspiration to the C standard and several of them (designated initializers, flexible array members, anonymous struct/union etc) have been adopted into the language itself with the C99 and C11 standards. One of the purposes for GNU C is actually to serve as an experimental playground where new languages features can be tried out live.
If you truly wish to add a new function to the actual C standard library, you would have to join the ISO working group and convince them that the function should be added to the language. Or alternatively find a member of the committee and convince them to speak in favour of the new function.
All this of course assuming you are a C programming veteran, or otherwise nobody will likely take you seriously.
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solved Procedure to include own functions to ANSI C Standard library