Someone else's "Apple ID" cannot gain access to your information.
Now if someone else has access to your Apple Account, that would give them a means to view and even alter data that you were synchronizing or backing up to iCloud. It is not a good idea to share an Apple Account with someone else, or to pick a password that would be easy for an attacker to guess. (Such as "password" or your birthday.)
If you think that your Apple Account is compromised, you should take steps to secure it.
If you think your Apple Account has been compromised - Apple Support
Likewise with other accounts – especially the ones that are likely to do the most damage in the wrong hands.