Hadith 1:

لأمالي للصدوق عن صفيّة بنت عبدالمطّلب : ـ لَمّا سَقَطَ الحُسَينُ عليه السلام مِن بَطنِ اُمِّهِ قالَ النَّبِيُّ صلى الله عليه و آله : يا عَمَّةُ، هَلُمّي إلَيَّ ابني. فَقُلتُ : يا رَسولَ اللّه ِ، إنّا لَم نُنَظِّفهُ بَعدُ . فَقالَ صلى الله عليه و آله : يا عَمَّةُ ! أنتِ تُنَظِّفينَهُ ؟! إنَّ اللّه َ تَبارَكَ وتَعالى قَد نَظَّفَهُ وطَهَّرَهُ

Narrated from Safiyah bint Abdul Muttalib,

"When Imam Husain (عليه السلام) was born, the Prophet (صلى الله عليه و آله) said, "O Aunt, Bring My Son quickly to Me". 

I (Safiyah) said, "I have not yet cleaned the child".

The Prophet (ص) said, "Will you clean him? Indeed Allah (تبارك و تعالى) has cleaned Him and Purified Him."

[Source: al-Amali, Shaikh Sadooq, Majalis. 28, Hadith. 5]

Hadith 2:

Narrated that Prophet Muhammad (صلى الله عليه وآله) said as part of a long hadith:

فلما ولد الحسين بن علي (ع) وكان مولده عشية الخميس ليلة الجمعة, أوحى الله عز وجل إلى مالك خازن النار أن أخمد النيران على أهلها لكرامة مولود ولد لمحمد, وأوحى إلى رضوان خازن الجنان أن زخرف الجنان وطيبها لكرامة مولود ولد لمحمد في دار الدنيا، وأوحى الله تبارك وتعالى إلى حور العين تزين وتزاورن لكرامة مولود ولد لمحمد في دار الدنيا, وأوحى الله عز وجل إلى الملائكة أن قوموا صفوفا بالتسبيح والتحميد والتمجيد والتكبير لكرامة مولود ولد لمحمد في دار الدنيا

When al-Husain ibn Ali (عليه السلام) was born, and his birth was on the night of Friday, Allah (عز وجل) revealed to Malik, the keeper of Hellfire, to extinguish the fires upon its inhabitants out of honor for the child born to Muhammad (صلى الله عليه وآله).

And He revealed to Ridwan, the keeper of Paradise, to adorn/decorate and perfume paradise out of honor for the child born to Muhammad (صلى الله عليه وآله) in the world.

And Allah (تبارك وتعالى) revealed to the Houri of Paradise to adorn/beautify themselves and visit each other out of honor for the child born to Muhammad (صلى الله عليه وآله) in the world.

And Allah (عز وجل) revealed to the angels to stand in rows glorifying, praising, magnifying, and exalting Him out of honor for the child born to Muhammad (صلى الله عليه وآله) in the world."

[Source: Kamal al-Deen, Shaikh Saduq, Vol. 1, Pg. 282]

Hadith 3:

Abu al-Qasim ibn Ala al-Hamadani, the representative of Imam al-Hasan al-Askari (عليه السلام), received a document telling that our master, Grandson of the Holy Prophet (صلى الله عليه وآله), Imam al-Husayn ibn Ali (عليه السلام), was born on the third of Shaban, therefore, you should observe fast on this day and recite the following supplication: 

خرج إلى أبي القاسم بن علاء الهمداني وكيل الإمام العسكري : أنّ مولانا الحسين عليه‌السلام ولد يوم الخميس لثلاث خَلونَ من شعبان ، فصمه وادع فيه بهذا الدعاء

اللّهُمَّ إِنِّي أَسْأَلُكَ بِحَقِّ المَوْلُودِ فِي هذا اليَوْمِ بِشَهادَتِهِ قَبْلَ اسْتِهْلالِهِ وَوِلادَتِهِ بَكَتْهُ السَّماء وَمَنْ فِيها وَالأَرْضُ وَمَنْ عَلَيْها وَلَمَّا يَطَأ لابَيَتْها ، قَتِيلِ العَبْرَةِ وَسَيِّدِ الاُسْرَةِ المَمْدُودِ بِالنُّصْرَةِ فِي يَوْمِ الكَرَّةِ المُعَوّضِ مِنْ قَتْلِهِ أَنَّ الأئِمَّةَ مِنْ نَسْلِهِ وَالشِّفاءَ فِي تُرْبَتِهِ وَالفَوْزَ مَعَهُ فِي أَوْبَتِهِ وَالأَوْصِياء مِنْ عُتْرَتِهِ بَعْدَ قائِمِهِمْ وَغَيْبَتِهِ حَتّى يُدْرِكُوا الأوْتارَ وَيَثْأَرُوا الثَّأرَ وَيُرْضُوا الجَبَّارَ وَيَكُونُوا خَيْرَ أَنْصارٍ ، صَلَّى الله عَلَيْهِمْ مَعَ اخْتِلافِ الليْلِ وَالنَّهارِ. اللّهُمَّ فَبِحَقِّهِمْ إِلَيْكَ أَتَوَسَّلُ وَأَسْأَلُ سُؤالَ مُقْتَرِفٍ مُعتَرِفٍ مُسِيٍ إِلى نَفْسِهِ مِمَّا فَرَّطَ فِي يَوْمِهِ وَأَمْسِهِ ، يَسْأَلُكَ العِصْمَةَ إِلى مَحَلِّ رَمْسِهِ ، اللّهُمَّ فَصَلِّ عَلى مُحَمَّدٍ وَعِتْرَتِهِ وَاحْشُرْنا فِي زُمْرَتِهِ وَبَوِّئْنا مَعَهُ دارَ الكَرامَةِ وَمَحَلَّ الإقامَةِ ، اللّهُمَّ وَكَما كَرَّمْتَنا بِمَعْرِفَتِهِ فَأَكْرِمْنا بِزُلْفَتِهِ وَارْزُقْنا مُرافَقَتَهُ وَسابِقَتَهُ وَاجْعَلْنا مِمَّنْ يُسَلِّمُ لاَمْرِهِ وَيُكْثِرُ الصَّلاةَ عَلَيْهِ عِنْدَ ذِكْرِهِ وَعَلى جَمِيعِ أَوْصِيائِهِ وَأَهْلِ أَصْفِيائِهِ المَمْدُودِينَ مِنْكَ بِالعَدَدِ الاِثْنَي عَشَرَ النُّجُومِ الزُّهَرِ وَالحُجَجِ عَلى جَميعِ البَشَرِ اللّهُمَّ وَهَبْ لَنا فِي هذا اليَوْمِ خَيْرَ مَوْهِبَةٍ وَانْجِحْ لَنا فِيهِ كُلَّ طَلِبَهٍ كَما وَهَبْتَ الحُسَيْنَ لِمُحَمَّدٍ جَدِّهِ وَعاذَ فُطْرُسُ بِمَهْدِهِ فَنَحْنُ عائِذُونَ بِقَبْرِهِ مِنْ بَعْدِهِ نَشْهَدُ تُرْبَتَهُ وَنَنْتَظِرُ أَوْبَتَهُ آمِينَ رَبَّ العالَمِينَ

O Allah: I ask You in the name of the one born on this day, the one promised with martyrdom before the beginning of his life and before his birth, the heavens and all their inhabitants wept for him; and so did the earth and those living one it even before His feet stepped on it, the one who is killed and cried upon (Qateel al-Abarat) and the master of the Family.

And the one who shall be supported with victory on the Day of Return. The one "The compensated for His killing is that the Imams are from his offspring, and cure in His soil, victory with Him when He returns, and also the return of the trustees (awsiyaa) from His offspring after their Qaim (عليه السلام) and after His occultation (Gaybah), so that they shall take revenge of their blood, and please the Almighty, and be the best supporters.

May Allah's blessings be upon them at every night and day.

O Allah, I request You by their rights; and I ask You with the asking of a confessing sinful person who has done evil to himself of what he has neglected in the past and the present.

He asks You for protection till his grave.

O Allah, Send blessings upon Muhammad and his progeny (عليهم السلام), and include us with his group and allow us to dwell in the House of Honor with him, and in the abode of residence.

O Allah, As you have honored us with His recognition (marefat), honor us with His nearness and grant us being close to Him and of priority to Him. And include us with those who submit to His command and those who send increased salutations upon Him when mentioning/remembering (Zekr) Him and all the trustees (Awsiya) that you have numbered as twelve - The shining stars and the proof (Hujjah) over all human beings."

O Allah, and grant us on this day the best of grants, and make all of our asks/requests on this day succesful, just as You gifted al-Husayn (عليه السلام) to Muhammad his grandfather (صلى الله عليه وآله). And just as the angel Futrus took refuge with His cradle, we are seeking refuge with His grave after him (i.e. his martyrdom) as we are witnessing His soil and waiting for His return.

Amen, Lord of the worlds

[Source: Misbah Al-Mutahajjid, Sheikh Toosi, Pg. 826-827]