How to clone a record of standard objects record with specific fields (not all the fields that comes when cloned)

You can create new object of the same type as your standard obj and add each field by hand:

//standard account obj we want to clone
Account accToClone = [SELECT Name, SomeOtherField FROM Account Limit 1];
//new account obj
Account acc = new Account();
acc.Name = accToClone.Name;