My younger brother is in the prison because some body made a false statement against him. Some body was in the jail and had a case against him. Now he lied and told the prosecutor that my brother is also involved, but my brother does not even know the person. Please tell us some Du'a in this time of trouble and make Du'a for us.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

No doubt that the best way to supplicate Allah is through remembering Him and feeling humble when asking Him. The Prophet (Sallallahu Alaihi wa Sallam) used to hasten to prayer whenever anything saddened him or became difficult to solve. Allah Says (interpretation of meaning): {And seek help in patience and As-Salât (the prayer) …} [2: 45].
The Prophet (Sallallahu Alaihi wa Sallam) also taught us to say when in desperate need or when in real trouble: "The Du'a of Yunis while inside the stomach of the fish. He said: "La Ilah Illa Anta Subhanaka Inni Kuntu Min Al Dhalimin" so Allah will answer the Du'a of any Muslim who asks with it no matter what he had asked for …" [ Ahmad ].
One could also in time of despair say: "La Ilah Illa Allah al-Adhim al-Halim La Ilaha Illa Allah Rabu al-Arshi al-Adhim. La Ilaha Illa Allah Rabu al-Samawat Wa Rabu al-Ardhi Rabu al-Arshi al-Kareem" [Reported by Imams al-Bukhari and Muslim ].
As for the prayer of need, its reported from the companions, read about it in Fatwa: 82384.
Know also that a Muslim will experience trials. But the reward comes by having patience when afflicted. Prophet Yusuf (Alaihi al-Salaam) was imprisoned for several years and the outcome of this was emancipation and triumph.
Allah knows best.