SharePoint online REST API Access

Hi Community,

I am planning to migrate a SharePoint 2013 on-premise based application to SharePoint-online. I need some help regarding user access to SharePoint lists.

Below the scenario

• My on-premise application interacting with 5 different lists using c# based CURD operations
• organization wise employees using this application 
• Using the Elevated privileges option we are maintaining user access through lists.

How do we manage user access if we re-write application to SharePoint online using REST API?

We can't give employees Edit/Contribute permission on my lists which many leads to security issues if the user directly access-list from UI

Please advise the possible solution in my case.