You can do this by developing a permissioned blockchain, which is a private network but only nodes with permission
are allowed to access the blockchain.
For this, first learn about the Fabric project by Hyperledger from https://hyperledger-fabric.readthedocs.io/en/release-1.1/
Understand the concepts.
This will help you understand how to develop a permissioned blockchain.
Then, develop the client to access the blockchain. Finally, deploy the smart contract in your blockchain.