Custom fields specific for a page

Create a custom page template that contains calls to your custom fields and then apply this new template to your Contact page.

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I’ve still created a custom page template and called my custom field but I don’t want them to show in the other (not in other tpl, i mean in oder editing-page views in the control panel)

If you use the Magic Fields plug-in you can customize the editing/entry page for each post type or page type showing just the fields you want.

that sounds good, I’ll have a try