How to connect to RDS My Sql Server instance which is in application VPC and Private subnets

Does your application live in the VPC private subnet as well and you want to access the application? If so, you can set up an Elastic Load Balancer that provides access to the application from the Internet.

If you want to provide access to the database from the Internet (which I wouldn't recommend), you could use a Network Load Balancer to do that. Best practice, you can deploy an API via API Gateway that fetches the results when someone uses it. This will allow you to provide access to the data without giving direct access to the database.