SF_9.2, SF_10.0, SF_10.1, SF_10.2, SF_11.0, SF_11.1, SF_11.2, SF_12.0, SF_12.1, SF_12.2, SF_13.0, SF_13.1, SF_13.2, SF_13.3, SF_14.0 - https://www.progress.com/documentation/sitefinity-cms/adding-layout-controls-to-pages-and-page-templates-webforms

query_layoutcontrols_page.cs

var pageData = manager.GetPageDataList()
    .Where(pd => pd.Status == Telerik.Sitefinity.GenericContent.Model.ContentLifecycleStatus.Live
    && pd.NavigationNode.Title == "Home")
    .SingleOrDefault();

var layoutControlOnPage = pageData.Controls
    .Where(c => c.ObjectType == typeof(LayoutControl).FullName
        && c.Caption == "Sample caption").FirstOrDefault();