You need to create a new/copied citation style in EndNote.
- Go to EndNote > Edit > Output Styles > Open Style Manager.
- Select the style that you wish to use and click Edit (e.g. Chicago 15th A).
- Go to Footnotes > Templates and remove the tick from the box "Include citations in bibliography"
- Save this style (File > Save As). You need to give it a different name (e.g. Chicago 15th A My Copy)
- Use this style for your paper