1.I created the SSH key in A server and that ssh key register(Copy SSH folder)in B server.
2.I am able to login the SFTP but while login it is assking password but I need without passwrd how to upload the file using sftp because I am doing automated the process means every day one file get uploaded in the directory
Also if u could let me know step by step it will be greate for me to configure SFTP between two server
If - as you say - you can't login with ssh public key authentication, your setup seems to be wrong.
Copying the ssh key to the remoteuser/.ssh directory is not enough; it needs to be appended to the ~/.ssh/authorized_keys file, and file and directory should have the recommended permissions.
You may want to use the -v (verbose) option to find some hints on what might be wrong.