The NeetoForm API allows you to list forms and read the submissions they receive, but it does not support creating submissions, and this is intentional.
Every submission is expected to come through the form itself, where validations such as required fields, conditional logic, and other rules are applied. Creating submissions directly through the API would skip all of them, so the responses you collect could no longer be trusted to match the rules you set up.
Also, NeetoForm is designed to collect responses using the forms you create. Using your own external form and sending data directly through the API would bypass that flow and effectively use NeetoForm only as a data storage layer, which is not a supported use case.
To collect responses, please share NeetoForm link and have respondents submit through the form.