Consultant, startup sent notice I owe them money for dishonest, unfinished work

They first didn’t signed any contract, I asked they didn’t bother , just email communication and they said it is legally bound by email

Now I invoiced them first for research work and then implementation . In ten NDA it says I can’t get a lawyer. The work I did was ongoing and like any software will have bugs or updates requirements if internal api change . After that I worked for few months, most of the last months work was experimentation . I in emails said yes I will complete task before any more payment and I did but it was asked to not be pushed to prod but I did spend time on Those tasks. Now they are asking to pay them back