All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Perhaps you are referring to the hadeeth narrated on the authority of Ibn ʻAbbaas which reads:
"While Jibreel (Archangel Gabriel) was sitting with the Prophet he heard a creaking sound above him. He lifted his head and said,'This is a gate opened in heaven today which had never been opened before.' An angel descended through it, so he said, 'This is an angel who came down to the earth who had never come down before.' He (the Angel) greeted them and said, 'Rejoice in two lights given to you which have not been given to any prophet before you: Faatihat Al-Kitaab (Quran Chapter 1) and the concluding verses of Soorah Al-Baqarah (Quran Chapter 2). You will recite a single letter of them but you will be granted it....'" [Muslim]
The phrase "but you will be granted it" in the hadeeth means that Allaah would grant the person whatever he has asked for like the case when the person recites the verse that reads (what means): {Guide us to the straight path} [Quran 1:6] (i.e. Allaah, The Exalted, accepts his supplication and guides him to it) or that which reads (what means): {...(We seek) Your forgiveness...} [Quran 2:285] (i.e. Allaah answers the supplication and forgives him). This is as far as the Faatihah and Baqarah chapters are concerned.
We could not find any specific hadeeth indicating that the supplications uttered after reciting the verse that reads (what means): {Our Lord, indeed we have heard a caller calling to faith, (saying), 'Believe in your Lord,' and we have believed...} [Quran 3:193] are answered. However, it is prescribed to supplicate after reciting the Quran in general. The Prophet said, "Recite the Quran and take it as a means through which you can supplicate Allaah, The Exalted, before a people would come who would take it as a means to ask others for their needs." [Ahmad - Al-Albaani graded it saheeh (sound)]
Scholars advised that supplications made after the recitation of the Quran are most likely to be accepted.
Allaah knows best.