Whenever I try to login to my Application, with different account (For example, If I have created my Application on firstname.lastname@example.org and I try to login to my Application with email@example.com ), It shows the following error:
"This app has reached its user limit. Contact the app developer and ask them to use the Dropbox API App Console to increase their app's user limit."
Have you done as it says, and increased the user limit of the app? By default, an app only allows its creator to access it. You have the ability to raise the limit to 500 users before moving it to production status.