Where is hex code of the "EOF" character?

The EOT byte (0x04) is used to this day by unix tty terminals to indicate end of input. You type it with a Ctrl + D (ie. ^D) to end input to shells or any other program reading from stdin.

However, as others have pointed out, this is distinct from EOF, which is a condition rather than a piece of data per se.

There was - a long long time ago - an End Of File marker but it hasn't been used in files for many years.

You can demonstrate a distant echo of it on windows using:

C:\>copy con junk.txt
Hello
Hello again
- Press <Ctrl> and <z>
C:\>dump junk.txt
junk.txt:
00000000  4865 6c6c 6f0d 0a48 656c 6c6f 2061 6761 Hello..Hello aga
00000010  696e 0d0a                               in..
C:\>

Note the use of Ctrl-Z as an EOT marker.

However, notice also that the Ctrl-Z does not appear in the file any more - it used to appear as a 0x1a but only on some operating systems and even then not consistently.

Use of ETX (0x03) stopped even before those dim and distant times.

There is no such thing as EOF. EOF is just a value returned by file reading functions to tell you the file pointer reached the end of the file.

There is no such thing as a EOF character. The operating system knows exactly how many bytes a file contains (this is stored alongside other metadata like permissions, creation date, and the name), and hence can tell programs that try to read the eleventh byte of a ten byte file: You've reached the end of file, there are no more bytes to read.

In fact, the "EOF" value returned for example by C functions like getchar is explicitly an int value outside the range of a byte, so it cannot possibly be stored in a file!

Sometimes, certain file formats insist on adding NUL terminators (probably because that's how strings are usually stored in C), though usually these delimit multiple records in a single file, not the file as a whole. And such decoration usually disqualifies a file from being considered a "text file".

ASCII codes like ETX and NUL date back to the days of teletypewriters and friends. NUL is used in C for in-memory strings, but this has no bearing on file systems.