Does this plugin Support Newspaper theme

Wrong question ??

You should ask whether the theme supports standard WP hooks and how/where.

Basically the plugin can insert any code anywhere on any WordPress page.
The question is what is the most elegant approach.

Ad Inserter uses standard WP hooks to insert codes:
https://adinserter.pro/faq/how-ad-inserter-works#automatic-insertion

You can use debugging function Show positions to see where these hooks are called and consequently where the positions for automatic insertion are:
https://adinserter.pro/documentation/debugging

If the wanted positions for automatic insertion are not available you can still insert there with insertion before/after HTML element:
https://adinserter.pro/documentation/insertion-before-inside-after-html-element

You did not post page address (with remote debugging enabled) so we can’t check:
https://www.ads-software.com/support/topic/ad-inserter-support-before-you-ask-for-help/