“The supplication of a Muslim for his brother in his absence will certainly be answered. Every time he makes a supplication for good for his brother, the angel appointed for this particular task says: ‘Ameen! May it be for you too’.” [Muslim].
Since the dua of the fasting person is accepted this is the best time to do it. But here is how you make it unique:
1. Do it for someone who wouldn’t expect it from you without telling that person to make it most sincere and for the sake of Allah.
2. Diversify the duas and people you make dua for so that you can be given different things. So in particular think of a person in each of the following categories and make dua for them daily:
a) A person who has good qualities but hasn’t been guided to faith. Make dua for guidance for that person so that perhaps Allah grants you further guidance.
b) A person who is involved in Islamic work, that Allah accepts from them and keeps them sincere so that perhaps Allah uses you for His cause and keeps you sincere.
c) A person who is committing a public sin. Make dua that Allah forgives that person. Imagine if the dua is accepted for a major public sin, then the angels will say ameen for you also and perhaps Allah will forgive you for both your public and private sins.
d) A person who is ill, that Allah grants him or her full health so that perhaps Allah will either heal you if you are sick or preserve your health for you if you are healthy.
e) A person who is struggling financially or suffering a worldly hardship, ask Allah to help that person so that perhaps Allah will help you in that same situation.
f) A person who has a particular blessing that you wish for, that Allah maintains that blessing upon that person without making it a means of taking him or her away from goodness in the hereafter so that perhaps Allah will grant it for you or maintain your blessings upon you without making them a means of harm for you.