Indian Contract Act, 1872 deals with the provisions of a contract. Section 11 of the Act lays down the essential requirements to form a valid contract and one of the most important conditions is the agreement of both the parties on the terms and conditions of the contract. You have mentioned that the agreement between the parties was not signed and one of the parties made payment according to the terms of the contract. Since the contract was not signed by the parties it cannot be called binding. Also, the other party changed the terms of the contract without the consent of the party who performed their part.
Here both the parties do not agree on the terms of the contract therefore it cannot be binding and whatever payment is done by the party can be recovered. You can file a suit before the court regarding recovery of the payment but you have no remedy against breach of contract by the other party as the contract was not legally binding.