What is the ruling in accordance to the Islamic law regarding the following supplication: The supplicant begins by praising Allah, The Almighty, with the greatest revelation sent to His Messenger (peace and blessings be upon him), which is Surah Al-Fatiha. Then, they invoke blessings upon the Messenger of Allah (peace and blessings be upon him), seek forgiveness for their sins, and ask for goodness in this world and the Hereafter for themselves, their parents, their family, and their relatives.                                                                 

After that, they proceed to send peace and blessings upon the pure souls, including the Messenger of Allah (peace and blessings be upon him), the prophets and messengers by name (Peace and Blessings of Allah be upon all of them) , the Rightly Guided Caliphs, the Prophet's family, descendants, companions, and wives, mentioning by name those they recall. Then, they extend their supplication to include the Tabi‘un (followers of the companions), the righteous of the Ummah, and its scholars, mentioning by name those they remember.

Following this, they recite the general supplication from the Quran, it states (What means): "Our Lord, forgive us and our brethren who preceded us in faith, and do not place in our hearts any resentment toward those who have believed. Our Lord, indeed You are Kind and Merciful." [Al-Hashr/10].                       

Then, they pray for the believers who strive for Islam and the support of Allah’s religion, specifically mentioning those with whom they share a bond of love. Lastly, they extend their supplication to the entire Ummah of the Prophet (PBUH), asking Allah for His mercy, forgiveness, and the goodness of this world and the Hereafter, and they include all of humanity in their prayer, asking Allah to guide them from the darkness of oppression and misguidance to the light of guidance and justice.

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Remembrance of Allah (Dhikr) and supplication (Du‘a) are among the greatest acts of worship and devotion, and their virtue is well established in numerous texts from the Quran and Sunnah, which are widely known.

Scholars unanimously agree on the permissibility of using supplications that have been transmitted (from the Prophet, peace and blessings be upon him) without any dispute. In this regard, Shafi‘i scholars have also permitted supplication using non-transmitted prayers. I.e. Al-Imam Al-Nawawi (may Allah have mercy on him) stated: "Al-Shafi‘i and his companions said: He is allowed to supplicate for whatever he wishes concerning matters of the Hereafter and this world, but supplications for the Hereafter are preferable. He may use supplications that are narrated for this occasion [i.e., in prayer] or others, and he is also allowed to supplicate with non-transmitted supplications for whatever he desires regarding worldly and religious affairs." [Al-Majmu‘ Sharh Al-Muhadhdhab/vol.3/pp.469].

Additionally, it is narrated from Nafi‘ that Abdullah Ibn ‘Umar (may Allah be pleased with all of them) reported: "The Talbiyah of the Messenger of Allah (peace and blessings be upon him) was: "Labbayk Allahumma labbayk, labbayka la sharika laka labbayk, inna al-hamda wa al-ni‘mata laka wa al-mulk, la sharika lak." (Here I am, O Allah, here I am. Here I am, You have no partner, here I am. Surely, all praise, grace, and dominion belong to You, You have no partner.)

He (Nafi‘) added: "Abdullah Ibn ‘Umar would add to his Talbiyah: ‘Labbayk, labbayk, labbayk wa sa‘dayk, wal-khayru biyadayk, wal-raghba’ ilayk wal-‘amal’ (Here I am, here I am, here I am and at Your service. All goodness is in Your hands, and to You is the desire and the effort)." [Abu Dawood]

Thus, a Muslim is not required to adhere to a specific formula for making a supplication, nor is any particular wording mandatory. Rather, a person may supplicate in any manner they choose for the goodness of this world and the Hereafter, as Allah Almighty Says (What means): "And when My servants ask you concerning Me, indeed I am near. I respond to the invocation of the supplicant when he calls upon Me." [Al-Baqarah/186]. As well He, The Almighty Says (What means): "And your Lord Says:" ‘Call upon Me; I Will Respond to you. Indeed, those who disdain My worship will enter Hell in humiliation." [Ghafir/60]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      The supplication mentioned in the question includes an opening with praises to Allah and His Messenger (peace and blessings be upon him), the recitation of Surah Al-Fatiha, and the mention of the names of prophets and righteous individuals, upon whom mercy descends when they are remembered. Besides, is no reprehensibility in doing any of this. Therefore, there is no harm in making the supplication mentioned in the question, as there is nothing prohibited in it. What is most primarily/essential in every supplication is the presence of the heart, sincerity, humility, and trust in Allah Almighty. And Allah Knows Best.