Is it possible to defend your rights?

Question

Work organization

Worked for one office. The amount of work for the month was predetermined in the contract. I did everything, signed the act, received the money. They offered to work for another month. Agreed. They said that the contract will be drawn up later (I know that I agreed in vain). In general, he worked for another month. At the end of this period, the head of the customer's programmers department said that I had done only 30% of the desired volume and that in order to receive full payment, I had to do another 70%. I was a little surprised and decided to end this not too comfortable working relationship. I arrived at the office and signed a new contract and an act of acceptance of work retroactively. However, in both the first and second papers, only two tasks were mentioned, and in fact I did four. I asked "why", and the head of the department mumbled something indistinct in response ("forgot" or "just did not enter").
Now a question. Can I somehow demand payment for all the work done? There is no contract for these parts. There is a fact of execution (these are two widgets that they already use), their discussion, amendments, correspondence from the beginning. department, team lead and project manager. There are a bunch of commits, there is a task in the internal crm of this enterprise, where I am mentioned as a performer. It is clear that they have planned this work and have also allocated a budget for it. I don’t want to conflict, but it’s still a shame - I had to sign the contract a second time.
Thank you.

Answer 1

I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! I will not start work without signing the contract! ... I will not start work without signing the contract! ... I will not start work without signing the contract! ...

Answer 2

Make a knight's move - prohibit the use of your intellectual property. You didn’t receive the money, and you didn’t transfer the rights. Avoid pandemonium with proving by ticks / correspondence, etc.
if you need to justify it normatively - write