What is the ruling on a man selling over his brother's sale in e-commerce, and does my aforementioned action fall under this noble Hadith, and is that considered stealing customers, and what is the expiation for this sin if it exists?

If the situation is as you described, and you are selling permissible goods, and you are truthful in describing them and mentioning their virtues without exaggeration or deception, then this is permissible, and there is no sin in it. It is not considered selling over another's sale, nor is it cheating or deception, nor is it stealing customers.