Which article should be used in documenting arguments to a software function

I would say all of those options are correct. There can be a subtle difference in meaning, though:

please specify a patch to the source directory: by using a, it is suggested that several different paths are possible, and that you need to provide one of those paths.

please specify the patch to the source directory: there is only one path that is correct, so we refer to this as the path.

Now suppose that the programme requires a path to a specific source directory, and only one path can be provided, which will be used throughout the programme. Then you could use the.

But suppose the path can be to any image file on the user's computer, whichever the user chooses; this might point to using a.

Both can be true at the same time, so it probably wouldn't matter much which you chose.