[Ethereum] Using Ethereum for data encryption

You cannot prevent anyone with access to the blockchain from reading state and executing code in any way they wish. You can encrypt data, but that doesn't prevent people from seeing it, just interpreting it.

Assuming you're happy with people who have stopped subscribing being able to access the data that was already available to them - something you fundamentally can't prevent anyway - there are a couple of ways you could achieve this.

One is to use standard multi-recipient public key encryption: Encrypt each message with a randomly generated key, then encrypt that key with the public key of each user who should be able to access it. When a user ceases their subscription, remove them from the set of active keys. When a new user subscribes, add them to the set, and encrypt the secrets of any past messages they should be able to access.

A slight variation may permit easier key management: Use one key for each 'epoch'. An epoch ends each time a user ends their subscription. Whenever you insert a message, encrypt it using the current epoch key (make sure to use an IV too, to prevent dictionary and known-plaintext attacks). Provide a keystore that lets users access the epoch keys for every epoch they're subscribed to; either off-chain, or by encrypting those keys with the public key of each user who's permitted to use them.

I only want the person who has access to the private key of the public key it was encrypted with to see the data. Is there a possible way to do it

Yes, you need to encrypt it before you send the data to the blockchain. Everything in the blockchain, including transactions, is public. So if you send the data in plaintext, anyone can see it.

At the moment I am using solidity's sha256() function to hash and store it in a mapping but like that anyone can decrypt it and get the data that I stored.

SHA256 is for hashing, not encryption. No one can "decrypt" something from a hash. (But as mentioned above, if you're hashing in the smart contract, then you've already shared the plaintext, so no one needs to "decrypt" anything.)