Let us see order of Imam asws regarding this, and the reward we get because of it. Sudooq wrote in his Amali in 27th Assembly

199 / 2 – حدثنا جعفر بن محمد بن مسرور (رحمه الله)، قال: حدثنا الحسين بن محمد بن عامر، عن عمه عبد الله بن عامر، عن إبراهيم بن أبي محمود، قال: قال الرضا (عليه السلام): إن المحرم شهر كان أهل الجاهلية يحرمون فيه القتال، فاستحلت فيه دماؤنا، وهتكت فيه حرمتنا، وسبي فيه ذرارينا ونساؤنا، وأضرمت النيران في مضاربنا، وانتهب ما فيها من ثقلنا، ولم ترع لرسول الله (صلى الله عليه وآله) حرمة في أمرنا. إن يوم الحسين أقرح جفوننا، وأسبل دموعنا، وأذل عزيزنا، بأرض (2) كرب وبلاء، أورثتنا الكرب والبلاء، إلى يوم الانقضاء، فعلى مثل الحسين فليبك الباكون، فإن البكاء يحط الذنوب العظام.

ثم قال (عليه السلام): كان أبي (صلوات الله عليه) إذا دخل شهر المحرم لا يرى ضاحكا، وكانت الكآبة تغلب عليه حتى يمضي منه عشرة أيام، فإذا كان يوم العاشر كان ذلك اليوم يوم مصيبته وحزنه وبكائه، ويقول: هو اليوم الذي قتل فيه الحسين (صلوات الله عليه) (1).


2 – Ja`far b. Muhammad b. Masrur رحمه اللّه narrated to us. He said: al Husain b. Muhammad b. `Aamir narrated to us from his uncle `Abdullah b. `Aamir from Ibrahim b. Abi Mahmud. He said: al Rida عليه السلام said: Muharram is the month in which the people of the Jahiliyyah would prohibit fighting but our blood was deemed lawful in it, our sanctity was violated in it, our offspring and our women were made captives in it, fire was ignited in our marquees and what was in them of our provision was plundered. And (despite our relationship) to the Messenger of Allah صلى اللّه عليه وآله, the sanctity in our affair was not observed. Surely on the day of Husain our eyelids were wounded, our tears made to flow, our beloved abased in the land of suffering and affliction (in the transcript: يا ارض – O land!). Suffering and affliction were rained down on us (or as per the manuscript: you rained suffering and affliction down on us). So, those who lament should lament on the like of Husain till the day of termination (i.e. the last day of this world), for surely the crying diminishes the great sins.

Then he عليه السلام said: When the month of Muharram would enter, my father (blessings of Allah be upon him) would not be seen laughing (smiling) and intense grief would overcome him until ten days had passed from it. So when it would be the tenth day, that day would be the day of his affliction and his mourning and his lamenting. And he would say: This is the day on which Husain عليه السلام was killed.

The narration is Authentic Inshallah. And I have given links to the narrators for those interested.

This narration is also present in Bihar-ul-Anwaar, 44/283-284