Use value of a dropdown field for an `include`
You don't need to (more specifically, you can't) nest Twig tags within other Twig tags. Ditch the inner Twig tag and its respective quotes, and just pass the variable directly into the outer Twig tag...

{% include entry.dropSubsection %}


That being said, I'm not sure this will achieve exactly what you're looking for. You may need to append .value as well...

{% include entry.dropSubsection.value %}