In the fifth section of the Holy Quran, in Surah An-Nisa, verse number 103, Allah Almighty says:

إِنَّ الصَّلـوۃَ کَانَتْ عَلَی الْمُوْمِنِیْنَ کِتَابًا مَّوْقُوْتًا

Allah Almighty has made prayer obligatory on believers at specific times. Therefore, it is necessary to offer prayers on time. However, if one is unable to offer prayers on time due to some excuse, illness, or compulsion, then Sharia has strictly ordered to offer it later, considering the importance of this worship.

Nowadays, it is an era of negligence. Firstly, many Muslims do not offer prayers at all. If they do pray sometimes, they do not pay attention to the conditions and etiquette, and the prayer, devoid of humility and reverence, presents only a sample of getting up and sitting down, and that's it.
It should have been that Muslims, upon missing the most important of worships, prayer,
 would be ashamed, repentant, and quickly offer their missed prayers according to the command of Sharia. Alas, a thousand pities that some self-proclaimed religious authorities, due to their lack of knowledge and understanding, have also subjected this matter to their absurd desires. Consequently, they have become victims of excess and deficiency.

One group has formed the opinion that there is no need to offer missed prayers; repentance alone is sufficient. On the other hand, some innovators, distorting this worship, have come up with the solution that offering all the prayers of a lifetime is very difficult, so they have invented a new prayer in the name of 'Qaza-e-Umri' (repayment of lifetime prayers) on the last Friday of Ramadan, and they say that by offering only four rak'ats in a specific way, all the prayers of a lifetime will be fulfilled.

Individuals of this school of thought spread false messages about this specific prayer during Ramadan, due to which a large segment of the Ummah falls prey to their deception. Ordinary, simple-minded Muslims also consider it correct and do not offer their prayers for the rest of their lives, and after offering this prayer, they think that there is no need for us to offer missed prayers anymore.
Whereas the view of Ahl al-Sunnah wal Jama'ah is completely different. It is that missed prayers are neither absolved merely by repentance nor are all prayers fulfilled by offering a specific four-rak'at prayer on the last Friday of Ramadan. Rather, it is necessary to offer missed prayers.
A few arguments are presented below.

 It is narrated from Hazrat Anas bin Malik (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said:

من نسی صلاۃ فلیصل اذا ذکرھا لا کفارۃ لھا الا ذالک 
Sahih Bukhari, Vol. 1, p. 84, Chapter: Whoever forgets a prayer

Translation: Whoever forgets to offer a prayer on time, it is necessary for him that whenever he remembers that he has not offered such and such prayer, then he should offer that prayer. There is no expiation for it other than that.

: While this hadith is present in Sahih Muslim with some difference in words 

عَنْ أَنَسِ بْنِ مَالِكٍ قَالَ قَالَ نَبِيُّ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ مَنْ نَسِيَ صَلَاةً أَوْ نَامَ عَنْهَا فَكَفَّارَتُهَا أَنْ يُصَلِّيَهَا إِذَا ذَكَرَهَا۔
Sahih Muslim: Vol. 1, p. 27

Translation: It is narrated from Hazrat Anas bin Malik (may Allah be pleased with him) that the Holy Prophet (peace and blessings of Allah be upon him) said that whoever forgets to offer a prayer or sleeps through it, then its expiation is that when he remembers, he should offer the prayer.

Sayings of the Companions 
Imam Malik (may Allah have mercy on him) narrates in his book Muwatta Imam Malik the saying of Hazrat Ibn Umar (may Allah be pleased with him)

عَنْ نَافِعٍ أَنَّ عَبْدَ اللَّهِ بْنَ عُمَرَ كَانَ يَقُولُ مَنْ نَسِيَ صَلَاةً فَلَمْ يَذْكُرْهَا إِلَّا وَهُوَ مَعَ الْإِمَامِ فَإِذَا سَلَّمَ الْإِمَامُ فَلْيُصَلِّ الصَّلَاةَ الَّتِي نَسِيَ ثُمَّ لِيُصَلِّ بَعْدَهَا الْأُخْرَى
Muwatta Imam Malik: 155
Translation: It is narrated from Hazrat Nafi' (may Allah have mercy on him) that Hazrat Abdullah bin Umar (may Allah be pleased with him) used to say that whoever forgets to offer a prayer, then remembers his missed prayer while praying with the Imam, then when the Imam says Salam, he should first offer the forgotten missed prayer, then after that, he should offer the other prayer.

Imam Tirmidhi (may Allah have mercy on him) has narrated a narration from Hazrat Abu Ubaidah bin Abdullah bin Masood in his Jami', so he says:

عَنْ أَبِي عُبَيْدَةَ بْنِ عَبْدِ اللَّهِ ابْنِ مَسْعُودٍ قَالَ قَالَ عَبْدُ اللَّهِ بْنُ مَسْعُودٍ إِنَّ الْمُشْرِكِينَ شَغَلُوا رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ عَنْ أَرْبَعِ صَلَوَاتٍ يَوْمَ الْخَنْدَقِ حَتَّى ذَهَبَ مِنْ اللَّيْلِ مَا شَاءَ اللَّهُ فَأَمَرَ بِلَالًا فَأَذَّنَ ثُمَّ أَقَامَ فَصَلَّى الظُّهْرَ ثُمَّ أَقَامَ فَصَلَّى الْعَصْرَ ثُمَّ أَقَامَ فَصَلَّى الْمَغْرِبَ ثُمَّ أَقَامَ فَصَلَّى الْعِشَاءَ۔
Jami' Tirmidhi p. 43

It is narrated from Hazrat Abu Ubaidah bin Abdullah bin Masood (may Allah be pleased with him) that Hazrat Ibn Masood (may Allah be pleased with him) said that on the day of the Battle of the Trench, the polytheists prevented the Messenger of Allah (peace and blessings of Allah be upon him) from offering four prayers until a portion of the night had passed, as much as Allah Almighty willed. Then the Prophet (peace and blessings of Allah be upon him) ordered Hazrat Bilal (may Allah be pleased with him), so he gave the Adhan and then said the Iqama, so he offered the Zuhr prayer, then he said the Iqama, so he offered the Asr prayer, then he said the Iqama, so he offered the Maghrib prayer, then he said the Iqama and offered the Isha prayer.