In the case of general supplication (du’aa’), it is not stipulated that it should be narrated in the Sunnah
Question

I heard one of the ignorant people offering supplication and one of the things that he said in his supplication was: “O Lord, do not make me dependent on any one or make me in need of anyone; make me independent of everyone, O You on Whom people rely and depend, Who is the One, the Only, the Self-sufficient, Who has no partner or son. O Allah, bring me back from misguidance to guidance and save me from every sin and trouble.” What is your opinion on this supplication?.
Praise be to Allah.You should differentiate between two types of supplication: 
1.The first type is restricted supplication, by which we mean that it is connected to a certain time or place or act of worship, or that Islam specifies a certain number or virtue and similar restrictions, such as the supplications that are narrated at the beginning of prayer, the adhkaar of morning and evening, the du’aa’s for sleeping, eating and so on.
In this type of supplication it is essential to limit it to that which is narrated in sharee’ah, without adding or subtracting anything. It is not permissible to make up any kind of supplication to take the place of that which is narrated in the Sunnah. 
This is what the Prophet (blessings and peace of Allah be upon him) taught to al-Bara’ ibn ‘Aazib (may Allah be pleased with him) when he said to him:
“When you go to bed, do wudoo’ as for prayer, then lie down on your right side, then say: ‘O Allaah, I have turned my face towards You and entrusted my affairs to You and relied completely upon You, out of hope and fear of You. There is no refuge or safe haven from You except with You. O Allah, I believe in Your Book which You have revealed, and in Your Prophet whom You have sent.’ Make these your last words. Then if you die that night, you will have died in a state of fitrah.” 
He said: I repeated them in the presence of the Prophet (blessings and peace of Allaah be upon him), and when I reached the words, ‘O Allah, I believe in Your Book which You have revealed’ I said: ‘I believe in Your Messenger whom You have sent,’ and he said: “No, ‘in Your Prophet whom You have sent.’” 
Narrated by al-Bukhaari (247) and Muslim (2710). 
Al-‘Allaamah al-Mu’allimi (may Allah have mercy on him) said in his book al-‘Ibaadah (p. 524): 
What a great loss is incurred by the one who forsakes the supplications that are proven in the Book of Allah or in the Sunnah of the Messenger of Allah (blessings and peace of Allah be upon him), so he hardly calls upon Allah by them, and he goes to something else and recites it regularly. Is this not wrongdoing and transgression? End quote. 
2.The second type is general supplication, which means asking Allah for needs both public and private, turning to Him and asking Him for what one needs and wants, such as supplication whilst prostrating, during the last third of the night and on the day of ‘Arafah and so on.
With regard to this kind of supplication, it is not essential that it be proven or narrated [in the texts], rather it is sufficient for the words of this supplication to be words that are acceptable and correct according to sharee’ah. There should be no transgression or overstepping the mark in supplication, and there should be no supplication that involves sin or severing the ties of kinship. 
It says in Fataawa al-Lajnah al-Daa’imah (24/203-204): 
The matter of supplication is broad in scope, so that each person may call upon his Lord for what he needs in ways that do not involve any sin. 
As for the du’aa’s and adhkaar that are narrated in texts, the basic principle concerning them is that we should adhere to the wording and numbers that are narrated. The Muslim should pay attention to that and adhere to it and not add to the specified number or add to the wording, or subtract anything from that, or change anything. End quote. 
It also says (24/275): 
The du’aa’s that are narrated in the Qur'aan and Sunnah are those which it is prescribed to adhere to, pay attention to, memorise and publicise. As for the other du’aa’s which all people say, they are not like that, and the best that may be said concerning them is that they are permissible, but they may contain phrases that are confusing or incorrect. End quote. 
It seems that the du’aa’ or supplication mentioned in the question comes under the heading of general supplication, and by examining its words and phrases, it seems that it is a permissible supplication and there is nothing wrong with it, and it does not seem to us that there was anything in it that is objectionable from a shar’i viewpoint; rather its words are sound and correct. So you should not denounce it or brand the one who says it as ignorant. 
See also the answer to questions no. 21561 and 75058. 
And Allah knows best.