Rather, it is permissible, recommended especially (if done) mournfully according to what you have recognized by what there is no exceeding upon it.
(al-Mustanad fi Sharh ilUrwat il-Wuthqa).

“So it is correct what we have claimed, that the prohibitive narrations are all weak in sanad.  So, the authoritative is free of opposition & the dislike of the fast of Ashura is not established, let alone its prohibition which was the view hold in al-Hada’iq of Yusuf al-Bahrani

Similarly Al-Khoie states:

فصحّ ما ادّعيناه من أنّ الروايات الناهية كلّها ضعيفة السند ، فتكون الآمرة سليمة عن المعارض ، فلم تثبت كراهة صوم يوم عاشوراء فضلا عن الحرمة التي اختارها في الحدائق ، بل هي جائزة ندباً ولا سيّما حزناً حسبما عرفت بما لا مزيد عليه

And the reliable(Muwaththaq) narration of Masada b. Sadaqa from Abu Abdillah(as), from Abu Jafar(as), who said that Imam Ali(as) said: “Fast on Ashura, the ninth and the tenth, for verily it atones for the sins of a year.”
(al-Mustanad fi Sharh il-Urwat il-Wuthqa)

As for the encompassing narrations commanding and recommending the fast of this day, they are many, like the authentic(Sahih) narration of al-Qaddah [from Abu Abdillah(as), from his father Abu Jafar(as), who said: The fasting of the day of Ashura is atonement for a year.

Imamiah scholar Abul-Qasim Al-Khoi states:

وأمّا الروايات المتضمّنة للأمر واستحباب الصوم في هذا اليوم فكثيرة ، مثل: صحيحة القدّاح : «صيام يوم عاشوراء كفّارة سنة» وموثّقة مسعدة بن صدقة : «صوموا العاشوراء التاسع والعاشر فإنّه يكفّر ذنوب سنة»

3rd narration
عن جعفر عن أبيه ( عليهما السلام ) قال : صيام يوم عاشوراء كفارة سنة

From Imam Ja’afar from his father (as): “The fasting of ‘Ashura removes the sins of a year.” (Tahtheeb al-Ahkam, Al-Istibsar & Wasael al-Shia).

[Sahih(authentic) as per al-Khoie].

2nd narration
عن ابي الحسن عليه السلام قال: صام رسول الله صلى الله عليه وآله يوم عاشورا

from Imam abu al-Hassan (as): “The messenger peace be upon him and his household fasted the day of ‘Ashura.” (Tahtheeb al-Ahkam & Al-Istibsar)

[Muawaththaq(reliable) as per al-Majlisi].

1st narration
أن عليا عليهما السلام قال: صوموا العاشوراء التاسع والعاشر فإنه يكفر ذنوب سنة

‘Ali (as) said: “Fast on ‘Ashura the ninth and tenth for it removes the sins of a whole year.” (Tahtheeb al-Ahkam,Al-Istibsar & Wasael al-Shia)
[Muawaththaq(reliable) as per al-Khoie]