What is the method or conditions for a legal guardian to manage the orphans' money without the consent of the younger siblings after the father's death?

The question is ambiguous. If what is meant is a method of guardianship over minors or acting as their agent, then if the father did not appoint a guardian for them, the judge takes charge of their affairs himself, or entrusts them to someone qualified for it. In Qatar, one can refer to the Endowments Authority (Hay’at al-Tarikāt) to manage the affairs of minors and consider what is best for them.