How to provide custom template declared inside my theme .theme file as variable inside page twig template
Presume you have something like: 

HOOK_theme($existing, $type, $theme, $path) {
  return [
    // mycustomtheme.html.twig
    'mycustomtheme' =&gt; [
      'variables' =&gt; [
        'var1' =&gt; NULL,
        'var2' =&gt; NULL,
        'var3' =&gt; NULL,
      ],
    ],
  ];
}  


You can preprocess the page.html.twig theme and add your theme output as a variable:

function HOOK_preprocess_page(&amp;$variables) {
  $var1 = 'foo';
  $var2 = 'bar';
  $var3 = 'baz';
  $variables['content']['customcontent'] = [
    '#theme' =&gt; 'mycustomtheme',
    '#var1' =&gt; $var1,
    '#var2' =&gt; $var2,
    '#var3' =&gt; $var3,
  ];
}


And then you should be able to print it on page.html.twig:

{{ content.customcontent }}