I try to configure my old iPhone with another account. Something went wrong, and now my iPhone is locked. How I can proceed to use with first registrations account?

Apple ID and Activation Lock

iCloud uses Apple ID credentials.

If you do not remember the Apple ID Password then follow the steps given in this Apple Article -> If you forgot your Apple ID password - Apple Support

If you do not remember the Apple ID then follow the steps given in this Apple Article -> If you forgot your Apple ID - Apple Support

If you are the owner or the owner has shared all information with you then to open Activation Lock:- If it is Activation locked, read here --> Turn off Activation Lock - Apple Support Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Learn how to remove a device from a previous owner's account.

If you are not the owner and do not have the Apple ID and Password then there is no way that you can get into this iPhone unless the original owner shares the Apple ID and password with you. If you are lucky you can get into this iPhone if they (owner) accidentally remove the device from their Apple ID.