<apex:column style="width: 200px">
    <apex:outputField value="{!Varsion.con.Additional_Email__c}" id="additionalEmail">
        <apex:inlineEditSupport event="ondblClick" showOnEdit="saveButton"/>
    </apex:outputField>
    <apex:facet name="header">CC Email</apex:facet>
</apex:column>

<apex:commandButton value="Save Changes" action="{!saveButton}" id="saveButton" />

public void saveButton(){
    List<ContentVersion> selectedIds = new List<ContentVersion>();
    List<ContentVersion> cver = new List<ContentVersion>();
    // Getting ids of selected records to be updated
    for(VersionWrapper vh: getIds()) {
        if(vh.selected == true) {
            selectedIds.add(vh.con);
        }
    }
    List<ContentVersion> contVerList = [Select Additional_Email__c from ContentVersion where Id IN: selectedIds];
    for(ContentVersion c:contVerList)
    {

        c.Additional_Email__c = 'Test'; // Here I want to get the values of edited email address...
        cver.add(c);
    }
    update cver;
    refreshGrid();
}