If the user enters a wrong key for AES decryption, some garbage data is generated. I want to verify the given decryption key and throw an error if the key is incorrect. How
Simplest approach is to add a magic number to the plaintext file data in a predictable location before encrypting; when decrypting, if the magic number is wrong, you used the wrong key. Downside to this approach is that it cannot validate the integrity/authenticity of the entire message.
To do that, use AES in an authenticated mode (e.g. AES-GCM) which gives stronger guarantees that the rest of the message was not tampered with.
Use an HMAC. The basic premise is that you run the plaintext through an HMAC, add the result to the plaintext and then encrypt. Then do the opposite when decrypting. If the plaintext and HMAC result match, then you know you've got the correct key.
OR, if you want to know prior to decryption, use the key material provided by the user to derive two further keys (using, say PBKDF2). Use one for encryption and another for an HMAC. In this case, encrypt first and then apply the HMAC using the second key. This way you can compute the HMAC and check if it matches before you decrypt.
One common way used to verify if a key is correctly entered, without revealing the actual key, is by use of a KCV (Key Check Value). When you create the key you would at the same time calculate the KCV, when the key is then entered manually, you can verify the entry by re-calcuylating the KCV. This is eg. used when entering keys manually into HSM's from physical key letters.
To calculate a KCV for an AES key you encrypt an empty (0x00) block with the key and the first 3 bytes of the resulting encrypted block is then the KCV.
Take a look here