I have a requirement where date and timestamp of a server has to be changed every day
This is ambiguous (and is a very bad design, since you are abusing the system). What actual file's metadata do you need to change? On what filesystem? Is it about
/proc/1234/ directory (if your process has pid 1234)? See proc(5).
(what if your server was on a read-only file system, e.g. some CDROM?)
BTW, you don't define what "updating a process" would mean. Even with a lot of imagination, I can't guess what you want.
Also, why is that needed? Why can't you change some other date & timestamp (of some data file, or even a row in a database) and check that? How do you detect the case when your "server executable" is on some weird filesystem which does not allow that, or has no valid mtime? Looks like some XY problem.
The goal is to have processes running while date is changed by an offset(number of days) for the running process.
I would then code a "shell-like" process (preferably in C or in some other language - Go, Ocaml, Rust, C++, Python, etc... - give access to the entire POSIX API, and at least to all system calls listed in syscalls(2), see also intro(2) and read some Unix programming book, at least ALP or something younger). That "shell-like" stuff would monitor, and kill, the actual server.
Notice also that most Java implementations are sort-of interpreted (by the JVM), in the sense that all such Java processes are running the same JVM executable, probably some