What script is included with the kernel source to patch a kernel?

update-kernel is not a script included with the kernel source; it is a distribution-specific package management command found on some Linux distros.

The patch-kernel script, located in the scripts/ directory of the Linux kernel source, automates downloading and applying incremental kernel patches. It calls the standard patch utility internally but provides a higher-level workflow tailored to kernel version management, making it the canonical tool bundled with the kernel source for this purpose.

apply-patch is not a script included in the standard kernel source tree.

patch is a standalone GNU utility that applies diff files, but it is not the script bundled inside the kernel source tree for patching kernels.