Is the reason suitors reject my sister that she used a "magic paper" from a sheikh with the aim of completing a previous engagement, and what is the solution to this problem?

It cannot be definitively stated that your sister's engagement was affected by magic (sihr). However, your mother and sister must repent to Allah Almighty for falling into this great evil, as the Prophet (peace be upon him) said: "He is not one of us who practices divination or has it practiced for him, or who practices sorcery or has it practiced for him, or who casts a spell or has a spell cast for him. And whoever comes to a soothsayer and believes what he says has disbelieved in what was revealed to Muhammad." Repentance involves abandoning the sin, regretting it, and resolving not to return to it. A sound repentance erases what came before it. The best cure for magic and protection from it is to diligently recite the prescribed remembrances (adhkar) and ruqyah, while relying on Allah.