re: "I have ended the contract with my client by mistake due to misunderstanding. How can I get back with my client and continue with our contract?"
There is no cost to a client to starting a new contract.
So this is a non-issue.
Because you now no longer have a contract with the client, you will no longer work on the client's project. So if the client desires your continued help, the client will create a new contract for you.
Tell the client:
"Bernice: Whoops! I accidentally clicked a button that closed the contract. If you will create a new contract like the one we were using and send me a Hire offer, I will accept the contract and continue my work on the project."
If the contract was closed by mistake, please reach out to your client directly about this and explain what has happened. This way you can discuss how you can continue working on the project.