The Prophet also said: "Whoever fasts one day in the sacred month Allah will grant him the reward of thirty days for every day." Is this Hadeeth authentic?
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger, may Allah exalt his mention as well as that of his family and all his companions.
At-Tabraani may Allah have mercy on him, reported that Ibn 'Abbaas, may Allah be pleased with him, narrated that the Prophet said:"Whoever fasts one day during the month of Muharram will get a reward of fasting 30 days." This is a fabricated narration as Shaykh Al-Albaani, may Allah have mercy on him, classified it in the As-Silssila Ath-Tha'eefah, Hadeeth number: 413. However, what is confirmed regarding the excellence of fasting during the month of Muharram is what is reported by Imaam Muslim that the Prophet said: "The best fasting after the month of Ramadan is during the month of Muharram, and the best prayer after the obligatory prayer is the optional night prayer." There are other narrations that encourage fasting during all the sacred months(i.e. Rajab, Thul-Qi'dah, Thul-Hijjah, Muharram).
Allah Knows best.