We have created one basic user on one of our server,we can login with admin user

When you log in with the basic user, what error are you getting? Incorrect credentials, or something like a 401 or 403?
Which URL are you logging into, Tempo or Designer or something else?

We are trying to login with designer and getting Incorrect credentials error.

Could you try doing a password reset on the account to make sure you have the correct credentials? Also make sure the user is part of the Designers group. By default basic users don't have access to Designer.

@ VijayK :Add that Basic User into Designer Group.
After that only basic user can access designer console with limited access.

we are getting error which is attached herewith while reset the user password.

Could you attach your application-server.log?

Application server log attached.

application-server.zip

@sandeepd- we already did this but no luck,getting "The username/password entered is invalid. Usernames and passwords are case sensitive."

Is the name of your basic user "Test1"? I see the following error for that user:

2015-10-15 13:01:23,898 [http-/0.0.0.0:8080-3] ERROR com.appiancorp.common.struts.BaseAction - Error executing action: The user [Test1] does not have sufficient privileges to perform the requested action because they are not in any role.
com.appiancorp.security.authz.AuthorizationException: The user [Test1] does not have sufficient privileges to perform the requested action because they are not in any role. (APNX-1-4188-001)

Make sure the user account is part of the Application Users group and that they have not been deactivated