It sounds like you want these files to be encrypted.
Someone already suggested encrypting them with GPG, but maybe you want the files themselves to also be isolated, even while their data is encrypted. In that case, consider an encrypted volume. I assume you’re familiar with LUKS - you can encrypt a partition with a different password and disable auto-mount pretty easily. But if you’d rather use a file-based volume, then check out VeraCrypt - it’s a FOSS-ish [1], cross-platform tool that provides this capability. The official documentation is very Windows-focused - the ArchLinux wiki article is a pretty useful Linux focused alternative.
Normal operation is that you use a file to store the volume, which can be “dynamic” with a max size or can be statically sized (you can also directly encrypt a disk partition, but you could do that with LUKS, too). Then, before you can access the files - read or write - you have to enter the password, supply the encryption key, etc., in order to unlock it.
Someone without the password but with permission to modify the file will be capable of corrupting it (which would prevent you from accessing every protected file), but unless they somehow got access to the password they wouldn’t be able to view or modify the protected files.
The big advantage over LUKS is ease of creating/mounting file-based volumes and portability. If you’re concerned about another user deleting your encrypted volume, then you can easily back it up without decrypting it. You can easily load and access it on other systems, too - there are official, stable apps on Windows and Mac, though you’ll need admin access to run them. On Android and iOS options are a bit more slim - EDS on Android and Disk Decipher on iOS. If you’re copying a volume to a Linux system without VeraCrypt installed, you’ll likely still be able to mount it, as dm-crypt has support for VeraCrypt volumes.
- 1 - It’s based on TrueCrypt, which has some less free restrictions, e.g.,
c. Phrase "Based on TrueCrypt, freely available at http://www.truecrypt.org/" must be displayed by Your Product (if technically feasible) and contained in its documentation.”
Anything that corrupts a single file would work. You could certainly change your own disk cloning binaries to include such functionality, but if someone were accessing your data directly via their own OS, that wouldn’t be effective. I don’t know of a way to circumvent that last part other than ensuring that the data isn’t left on disk when you’re done. For example, you could use a ramdisk instead of non-volatile storage. You could delete or intentionally corrupt the volume when you unmount it. You could split the file, storing half on your USB flash drive and keeping the other half on your PC. You could XOR the file with contents of another file (e.g., one on your USB flash drive instead of on your PC) and then XOR it again when you need to access it.
What sort of attack are you trying to protect from here?
If the goal is plausible deniability, then it’s worth noting that VeraCrypt volumes aren’t identifiable as distinct from random data. So if you have a valid reason for having a big block of random data on disk, you could say that’s what the file was. Random files are useful because they are not compressible. For example, you could be using those files to test: network/storage media performance or compression/hash/backup&restore/encrypt&decrypt functions. You could be using them to have a repeatable set of random values to use in a program (like using a seed, but without necessarily being limited to using a PRNG to generate the sequence).
If that’s not sufficient, you should look into hidden volumes. The idea is that you take a regular encrypted volume, whose free space, on disk, looks just like random data, you store your hidden volume within the free space. The hidden volume gets its own password. Then, you can mount the volume using the first password and get visibility into a “decoy” set of files or use the second password to view your “hidden” files. Note that when mounting it to view the decoy files, any write operations will have a chance of corrupting the hidden files. However, you can supply both passwords to mount it in a protected mode, allowing you to change the decoy files and avoid corrupting the hidden ones.