This means changing the order of the columns in the Sharepoint List Creation and Editing forms using either the Sharepoint 2010 Client Object Model or the Sharepoint 2010 Web Services.
2 answers
You can change the display order of fields on forms programmatically or via the web interface in cases where the ListFormWebPart web part is used for display.
Let me remind you that in the default forms, ListFormWebPart is responsible for generating fields. But if you create a new form, then DataFormWebPart takes over the function of generating html fields. In addition, each individual field is generated by the FormField control. Customizing a form becomes much easier when using a DataFormWebPart, but if you add a new field, you will have to add it to the form yourself using the FormField element. Also, when using DataFormWebPart, the settings for displaying fields do not affect the form.
PowerShell is almost always more convenient in solving such issues, especially if you have access to the server. Here is a working example.