<Root>/sitecore/content/Articles</Root>

public class Article : SearchResultItem
{
    [IndexField("_uniqueid")]
    public string ItemPath { get; set; }

    [IndexField("_group")]
    public string Id { get; set; }

    [IndexField("title")]
    public string Title { get; set; }

    [IndexField("publisheddate")]
    public DateTime PublishedDate { get; set; }

    [IndexField("summary")]
    public string Summary { get; set; }

}

list.Where(c => c.PublishedDate.Year == 2017).ToList();

public class ComputedYearField: IComputedIndexField

{
 public string FieldName { get; set; }
 public string ReturnType { get; set; }

 public object ComputeFieldValue(IIndexable indexable) {

  Item item = (indexable as SitecoreIndexableItem);

  if (item != null)
  {

   // check if item is an Article
   if(item.TemplateID == "YOURARTICLETEMPLATEID")
   {
    // extract the year from PublishDate field
    var dateField = (DateField)item.Fields["PublishedDate"];
    var itemDate = Sitecore.DateUtil.IsoDateToDateTime(dateField.Value);

    return itemDate.Year
   }
  }
  return null;
 }

}

<fields hint="raw:AddComputedIndexField">
<field fieldName="ComputedYear" returnType="int">
     MyProjectNamespace.ComputedYearField,MyProjectNamespace
</field>
</fields>

list.Where(c => c.ComputedYear == 2017).ToList();

var dateStart = new DateTime(year, 1, 1);
var dateEnd = new DateTime(year, 12, DateTime.DaysInMonth(year,12));

list.Where(x => x.Date.Between(dateStart, dateEnd, Inclusion.Both));
// or
// list.Where(x => x.Date>=dateStart && x.Date<=dateEnd);