What is the best LMS on premise software that can allow you to post local videos and see progress of students video viewing?

You can try iSpring Learn, it has on-premise version which fully integrates with your IT ecosystem.

This version has all of the SaaS version features, you can organize different types of trainings and track student’s performance. All the LMS data is stored on your internal servers and it prevents external breaches or unauthorized use.

The software engineers help you to deploy this on-premise version, so you don’t need to do anything yourself.