Threatened to sue by client

We developed a website for a certain client and we finished it with minor revisions.The contract is for the website. And then they want to integrate a booking system which is not stated in the contract. We did the booking system without initial down payment hoping that they will pay just like they did in the website. The problem now is that they are harassing us to finish it, but when we told them that we will give them another contract and asked for the down payment they got mad and told us that we have to finish it first before they pay or they will sue us. They said that the contract is meeting of the minds. We are hopeless that they will pay. What could we do?

Can you prove they have ordered the booking system?
Otherwice you have problem to demand pay for what you do.

" They said that the contract is meeting of the minds. "
??? Do they claim the booking system is suppoused to be included in what they have paid allready.
I can't interprete that without have seen the contract text

IF the contract don't say it's included, sure DON'T DELIVER before they have paid at least most of it. To you or to someone trustworthy who hold the money until you have delivered, if the customer demand that security.

The problem is booking is not included in the previous
transaction but it has been delivered and they are
already using it.And now they have a lot of revision
and we are doing it so we can collect the payment.

Oh you have delivered it allready.

"And now they have a lot of revision
and we are doing it so we can collect the payment."
What's the problem then? Do they say No to you geting paid?